Hecke algebras

lmfdb/hecke_algebras/__init__.py

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+# -*- coding: utf-8 -*-
+from lmfdb.base import app
+from lmfdb.utils import make_logger
+from flask import Blueprint
+
+hecke_algebras_page = Blueprint("hecke_algebras", __name__, template_folder='templates', static_folder="static")
+hecke_algebras_logger = make_logger(hecke_algebras_page)
+
+
+@hecke_algebras_page.context_processor
+def body_class():
+    return {'body_class': 'hecke_algebras'}
+
+import main
+assert main
+
+app.register_blueprint(hecke_algebras_page, url_prefix="/ModularForm/GL2/Q/HeckeAlgebra")

lmfdb/hecke_algebras/hecke_algebras_stats.py

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+# -*- coding: utf-8 -*-
+from lmfdb.base import app
+from lmfdb.utils import make_logger, comma
+from lmfdb.base import getDBConnection
+
+logger = make_logger("hecke_algebras")
+
+def db_heckestats():
+    return getDBConnection().hecke_algebras.hecke_algebras.stats
+
+def hecke_algebras_summary():
+    heckestats = db_heckestats()
+    hecke_knowl = '<a knowl="hecke_algebra.definition">Hecke algebras</a>'
+    level_knowl = '<a knowl="mf.elliptic.level">level</a>'
+    weight_knowl = '<a knowl="mf.elliptic.weight">weight</a>'
+    gamma0_knowl = '<a knowl="group.sl2z.subgroup.gamma0n">$\Gamma_0$</a>'
+    level_data = heckestats.find_one('level')
+    number = level_data['total']
+    max_level = level_data['max']
+    weight_data = heckestats.find_one('weight')
+    max_weight = weight_data['max']
+    return ''.join([r'The database currently contains {} '.format(comma(number)),
+                    hecke_knowl,'. The largest ', level_knowl, ' for ' , gamma0_knowl , ' is {}, '.format(comma(max_level)),
+                    'the largest ', weight_knowl, ' is {}.'.format(comma(max_weight))])
+
+@app.context_processor
+def ctx_hecke_algebras_summary():
+    return {'hecke_algebras_summary': hecke_algebras_summary}

lmfdb/hecke_algebras/templates/hecke_algebras-error.html

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+{% extends "homepage.html" %}
+
+{% block content %}
+<div>
+<input type=button value="Back" onClick="history.go(-1)">
+</div>
+{% endblock %}

lmfdb/hecke_algebras/templates/hecke_algebras-index.html

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+{% extends "homepage.html" %}
+{% import 'color.css' as color %}
+{% block content %}
+{% if BETA %}
+<div>
+{{ KNOWL_INC('dq.hecke_algebras.extent') }}
+</div>
+
+<style type="text/css">
+.error_message {
+   padding: 4px;
+   color: {{color.red}};
+   font-size: 120%;
+   font-weight: bold;
+   margin: 20px;
+}
+</style>
+{% if err_msg %}
+<p class="error_message">
+{{err_msg}}
+</p>
+<p>
+  <input type=button value="Search again" onClick="history.go(-1)">
+</p>
+{% endif %}
+
+<h2> Browse {{ KNOWL('hecke_algebra.definition', title='Hecke Algebras') }} for {{ KNOWL('group.sl2z.subgroup.gamma0n', title='$\Gamma_0$') }}</h2>
+
+<p>
+By {{ KNOWL('mf.elliptic.level', title='Level') }}: 
+{% for rnge in info.lvl_list %}
+<a href="?level={{rnge}}">{{rnge}}</a>
+{% endfor %}
+</p>
+<p>
+By {{ KNOWL('mf.elliptic.weight', title='Weight') }}:
+{% for rnge in info.wt_list%}
+<a href="?weight={{rnge}}">{{rnge}}</a>
+{% endfor %}
+</p>
+
+<p>
+Some of our favourite {{ KNOWL('hecke_algebra.definition', title='Hecke Algebras') }}:
+{% for rnge in info.favourite_list %}
+<a href="?label={{rnge}}">&nbsp; {{rnge}} &nbsp;</a>
+{% endfor %}
+</p>
+<p>A <a href={{url_for('.random_hecke_algebra')}}>random Hecke Algebra</a> from the database.
+<br>
+</p>
+
+
+
+<h2> Find a specific {{ KNOWL('hecke_algebra.definition', title='Hecke Algebra') }} by {{KNOWL('hecke_algebras.label', title='label')}}</h2>
+
+<form>
+<input type='text' name='label' placeholder='1.12.1'>
+<button type='submit'>Label</button>
+<br><span class="formexample">e.g. 1.12.1, 139.2.1, 11.2.1</span>
+</form>
+
+
+<h2> Search </h2>
+
+<p>Please enter a value or leave blank:</p>
+<form>
+<table>
+<tr>
+<td align= right>{{ KNOWL('mf.elliptic.level', title='Level') }}:</td>
+<td><input type='text' name='level' placeholder='3' size=10>
+<td><span class="formexample"> e.g. 3 or 2-5</td>
+</tr>
+
+<tr>
+<td align= right>{{ KNOWL('mf.elliptic.weight', title='Weight') }}:</td>
+<td><input type='text' name='weight' placeholder='1' size=10>
+<td><span class="formexample"> e.g. 2 or 10-100</td>
+</tr>
+<tr>
+<td align= right>Number of {{ KNOWL('mf.elliptic.hecke-orbit', title='Hecke orbits') }}:</td>
+<td><input type='text' name='num_orbits' placeholder='4' size=10>
+<td><span class="formexample"> e.g. 4 or 1-3</td>
+</tr>
+<tr>
+<td align= right>{{ KNOWL('mf.elliptic.hecke-orbit-label', title='Hecke orbit label') }} :</td>
+<td><input type='text' name='orbit_label' placeholder='1.12.1.1' size=10>
+<td><span class="formexample"> e.g. 1.12.1.1 or 139.2.1.2</td>
+</tr>
+
+<tr>
+<td align= right>Mod &#x2113; and &#x2113;-adic information:</td>
+<td><input type='text' name='ell' placeholder='5' size=10>
+<td><span class="formexample"> e.g. 5, any prime &#x2113;$<17$</td>
+</tr>
+
+<tr>
+<td colspan=3><button type='submit' value='Search'>Search</button>
+</td>
+</tr>
+</table>
+</form>
+{% else %}
+<div>This data is not yet available.</div>
+{% endif %}
+{% endblock %}

lmfdb/hecke_algebras/templates/hecke_algebras-search.html

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+{% extends 'homepage.html' %}
+{% block content %}
+
+<h2> Further refine search </h2>
+<form id='re-search'>
+<input type="hidden" name="start" value="{{info.start}}"/>
+<table border="0">
+<tr>
+<td align=left>{{ KNOWL('mf.elliptic.level', title='Level') }}</td>
+<td align=left>{{ KNOWL('mf.elliptic.weight', title='Weight') }}</td>
+<td align=left>Number of {{ KNOWL('mf.elliptic.hecke-orbit', title='Hecke orbits') }}</td>
+</tr>
+
+<tr>
+<td align=left><input type='text' name='level' size=10 value="{{info.level}}"></td>
+<td align=left><input type='text' name='weight' size=10 value="{{info.weight}}"></td>
+<td align=left><input type='text' name='num_orbits' size=10 value="{{info.num_orbits}}"></td>
+</tr>
+
+
+
+<tr>
+<td align= left>{{KNOWL('mf.elliptic.hecke-orbit-label', title='Hecke orbit label')}}:</td>
+<td align= left>Mod &#x2113; and &#x2113;-adic:</td>
+</tr>
+<tr>
+<td align=left><input type='text' name='orbit_label' size=10 value="{{info.orbit_label}}"></td>
+<td align=left><input type='text' name='ell' size=10 value="{{info.ell}}"></td>
+</tr>
+
+<tr>&nbsp;</tr>
+<tr>
+<td align=left colspan=2>Maximum number of Hecke Algebras to display</td>
+<td align=left><input type='text' name='count' size=10 value={{info.count}}></td>
+<td><button type='submit' size=10  value='refine'>Search again</button></td>
+</tr>
+</table>
+</form>
+
+{% if info.err is defined %}
+    <h2>Error</h2>
+    <div>
+    <!--  {{ info.err|safe }}-->
+    Either modify your search above or go <input type=button value="Back" onClick="history.go(-1)">
+    </div>
+{% else %}
+    {% if info.report == "no matches" %}
+        <h2> No matches</h2>
+    {% else %}
+        <h2> Results ({{info.report}})
+        {% if info.start > 0 %}
+            <a href="#" class="navlink"
+               onclick="decrease_start_by_count_and_submit_form('re-search');return
+                        false">Previous</A>
+        {% endif %}
+        {% if info.more > 0 %}
+            <a href="#" class="navlink" onclick="increase_start_by_count_and_submit_form('re-search');return false">Next</A>
+        {% endif %}
+        </h2>
+        <table>
+        <tr>
+        {% if info.ell %}
+        <th>{{KNOWL('hecke_algebras.orbit_label', title='Orbit label')}}</th>
+        <th>{{ KNOWL('mf.elliptic.level', title='Level') }}</th>
+        <th>{{ KNOWL('mf.elliptic.weight', title='Weight') }}</th>
+        </tr>
+        {% for a in info.hecke_algebras %}
+            <tr>
+            <td align='left'><a href="{{url_for('hecke_algebras.render_hecke_algebras_webpage', label=a.label)}}#{{a.index}}">{{a.orbit_label}} </a></td>
+            <td>{{a.level}}</td>
+            <td>{{a.weight}}</td>
+            </tr>
+        {% endfor %}
+
+        {% else %}
+        <th>{{KNOWL('hecke_algebras.label', title='Label')}}</th>
+        <th>{{ KNOWL('mf.elliptic.level', title='Level') }}</th>
+        <th>{{ KNOWL('mf.elliptic.weight', title='Weight') }}</th>
+        <th>Number of {{ KNOWL('mf.elliptic.hecke-orbit', title='Hecke orbits') }}</th>
+        </tr>
+        {% for a in info.hecke_algebras %}
+            <tr>
+            <td align='left'><a href="{{url_for('hecke_algebras.render_hecke_algebras_webpage', label=a.label)}}">{{a.label}} </a></td>
+            <td>{{a.level}}</td>
+            <td>{{a.weight}}</td>
+            <td>{{a.num_orbits}}</td>
+            </tr>
+        {% endfor %}
+        {% endif %}        
+        </table>
+        <hr>
+        {% if info.start > 0 %}
+            <a href="#" class="navlink" onclick="decrease_start_by_count_and_submit_form('re-search');return false">Previous</A>
+        {% endif %}
+        {% if info.more > 0 %}
+            <a href="#" class="navlink" onclick="increase_start_by_count_and_submit_form('re-search');return false">Next</A></td>
+        {% endif %}
+        <br>
+
+        <form>
+        Download all search results for
+        <input type="submit" name="submit" value="gp">
+        <input type="submit" name="submit" value="sage">
+        <input type="submit" name="submit" value="magma">
+        <input type="hidden" name="download" value="1"/>
+        <input type="hidden" name="query" value="{{info.query}}"/>
+        </form>
+    {% endif %}
+{% endif %}
+<!--<br>-->
+<!--{% if DEBUG %}-->
+<!--<p class="tex2jax_ignore">  Results for database query {{ info.query }}</p>-->
+
+<!--{% endif %}-->
+
+{% endblock %}

lmfdb/hecke_algebras/templates/hecke_algebras-single.html

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+{% extends "homepage.html" %}
+
+{% block content %}
+
+{% set KNOWL_ID = "hecke_algebra.%s"|format(info['label']) %}
+<h2>{{ KNOWL_INC(KNOWL_ID+'.top',title='') }}</h2>
+
+{% if info.num_orbits==0 %}
+
+<div>The Hecke algebra with {{KNOWL('hecke_algebras.label', title='label')}} ${{info.label}}$ is trivial: there are no modular forms of level ${{info.level}}$ and weight ${{info.weight}}$.</div>
+
+{% else %}
+<table>
+    <tr><td align=right>{{ KNOWL('mf.elliptic.level', title='Level') }}:</td><td>{{info.level}}</td></tr>
+    <tr><td align=right>{{ KNOWL('mf.elliptic.weight', title='Weight') }}:</td><td>{{info.weight}}</td></tr>
+    <tr><td align=right>{{KNOWL('hecke_algebras.dimension', title='Dimension')}}:</td><td>{{info.dim_alg}}</td></tr>
+    <tr><td align=right>{{KNOWL('hecke_algebras.label', title='Label')}}:</td><td>{{info.label}}</td></tr>
+</table>
+
+
+
+{% if info.orbits %}
+<h2>{{ KNOWL('mf.elliptic.hecke-orbit', title='Hecke orbits') }}</h2>
+<div><table>
+    <tr><td align="center">{{KNOWL('hecke_algebras.label', title='Label')}}</td><td align="center">Dimension</td></tr>
+    {% for j in info.orbits %}
+        <tr><td align="center"><a href="#{{loop.index}}">{{j.orbit_label}}</a></td><td align="center">{{j.dim}}</td></tr>
+    {% endfor %}
+</table></div>
+
+</br>
+    {% for j in info.orbits %}
+        <hr>
+        <h3><a name="{{loop.index}}">{{ KNOWL('mf.elliptic.hecke-orbit', title='Hecke orbit')}} {{j.orbit_label}}</a></h3>
+        <table>
+        <tr><td align= right>{{ KNOWL('mf.elliptic.hecke-orbit', title='Hecke orbit')}} dimension:</td><td valign= bottom>{{j.dim}}</td></tr>
+        {% if j.hecke_op_display == [] %}
+            <tr><td align= right valign= top>Hecke operators:</td><td>Download the avaliable Hecke operators $T_n$ for $n\leq {{j.num_hecke_op}}$ for {% for e in j.download_op %} <a href="{{e[1]}}">{{e[0]}}</a>{% if not loop.last %},  {% endif %}{% endfor %}</td></tr>
+        {% else %}
+            <tr rowspan=2><td align= right valign= top>Hecke operators:</td><td>
+            {% for m in j.hecke_op_display %}
+                $T_{ {{m[0]}}} ={{m[1]}}${% if not loop.last %},  {% else %}...{% endif %}
+            {% endfor %}</td></tr>
+            <tr><td></td><td>Download the avaliable Hecke operators $T_n$ for $n\leq {{j.num_hecke_op}}$ for {% for e in j.download_op %} <a href="{{e[1]}}">{{e[0]}}</a>{% if not loop.last %},  {% endif %}{% endfor %}</td></tr>
+        {% endif %}
+        {%if j.Zbasis %}
+            {% if j.gen_display == [] %}
+                <tr><td align= right valign= top>$\Z$-basis:</td><td>Download the basis for {% for e in j.download_gen %} <a href="{{e[1]}}">{{e[0]}}</a>{% if not loop.last %},  {% endif %}{% endfor %}</td></tr>
+            {% else %}
+                <tr><td align= right valign= top>$\Z$-basis:</td><td>
+                {% for n in j.gen_display %}
+                    ${{n}}${% if not loop.last %},  {% endif %}
+                {% endfor %}</td></tr>
+                <tr><td></td><td>Download the basis for {% for e in j.download_gen %} <a href="{{e[1]}}">{{e[0]}}</a>{% if not loop.last %},  {% endif %}{% endfor %}</td></tr>
+            {% endif %}
+                <tr><td align= right>Discriminant as $\Z$-algebra:</td><td>
+                {% if j.discriminant ==1 %}
+                    1
+                {% else %}
+                    ${{j.discriminant}}={% for k in j.disc_fac %}{{k[0]}}{% if k[1] !=1 %}^{ {{k[1]}} }{% endif %}{% if not loop.last %}\cdot  {% endif %}{% endfor %}$
+                {% endif %}</td></tr>
+                <tr><td align= right>Inner twists:</td><td>{{j.inner_twists}}</td></tr>
+                <tr><td align= right>$\Q$-basis:</td><td>${% for n in j.Qbasis %}T_{ {{n}} }{% if not loop.last %},  {% endif %}{% endfor %}$</td></tr>
+                <tr><td align= right>{{KNOWL('hecke_algebras.generator', title='Generator')}} as $\Q$-algebra:</td><td>${% for n in j.Qalg_gen %}T_{ {{n}} }{% if not loop.last %},  {% endif %}{% endfor %}$</td></tr>
+        {% endif %}
+        </table>
+        <p>&nbsp;&nbsp;&nbsp;&#x2113;-adic and mod &#x2113; data for &#x2113;=
+        {% for i in info.l_adic %}
+             <a href="{{url_for('hecke_algebras.render_hecke_algebras_webpage_l_adic', orbit_label=j.orbit_label, prime=i)}}">{{i}}</a>{% if not loop.last %}, {% endif %}
+        {% endfor %}</p>
+    {% endfor %}
+{% endif %}
+
+{% endif %}
+
+{% endblock %}