Noncongruence subgroups and Maass Waveforms.

This repository contains Examples, code and Data for the paper "Noncongruence Subgroups and Maass waveforms"

You can make basic queries etc. against the database of subgroups without having SAGE (http://www.sagemath.org) or PSAGE (https://github.com/fredstro/psage) installed but certain extra features will only be available through PSAGE.

Examples of Maass forms and eigenvalues are available in the /examples directory:

• examples/examples_eigenvalue_tables.py -- data corresponding to Tables of non-exceptional eigenvalues
• examples/examples_exceptional.py -- data for Tables of exceptional eigenvalues.

Database of subgroups

The database of subgroups is available through MongoDB and to interact with it you need access to the following:.

1. MongoDB
2. Python

Setup database:

1. Install mongodb: See e.g. http://www.hongkiat.com/blog/webdev-with-mongodb-part1/ for installation in various systems.
2. Untar the database files in subgroupsdb.tar:

cd data tar -xvf subgroupsdb.tar this creates a directory 'subgroups' and you can now:

3. Insert all data into your local mongo database:

mongorestore -d subgroups data/subgroups/ (This was created using `mongodump -d

Docker

If you can't install mongodb on your machine but have docker installed you can install it and recreate the database by the following steps:

1. follow the steps above and untar the subgroups directory in /tmp (otherwise change /tmp below))

2. docker pull mongo

3. docker run --name mongo-503 -p 27017:27017 -v /tmp:/data/ -d mongo

4. docker exec mongo-503 sh -c 'mongorestore -d subgroups /data/subgroups'

You will now have a running mongodb at port 27017

Use without Sage

It is generally considered best to setup and run python modules in a virtual environment of some kind. Which version you use depends on your preferences. You can use either of

1. virtualenv wrapper: https://virtualenvwrapper.readthedocs.io/
2. venv
3. conda

venvwrapper

1. Install virtualenv wrapper: https://virtualenvwrapper.readthedocs.io/
2. Make a virtual environment

mkvirtualenv noncong This also activates the environment.

venv

1. python3 -m venv /path/to/new/virtual/environment
2. source /path/to/new/virtual/environment/bin/activate

conda 1conda create -n noncong python=3

After this you just need to install the requirements:

pip install -r requirements.txt

Access the database

See the mongoengine docs: http://mongoengine.org/ for information on how to query the database through the models. Available models:

subgroups.models.Signatures --> Valid signatures of groups in the database subgroups.models.ConjugacyClassesPSL --> Conjugacy classes (where we have complete information) subgroups.models.Subgroups --> Subgroups

ipython In [1]: import noncong

In [2]: noncong.subgroups.models.Subgroup.objects.filter(genus=0,index=10).count() 255

In [3]: g=noncong.subgroups.models.Subgroup.objects.filter(index=10).first();g

Out[4]: Subgroup of PS(2,Z) of signature (10;0,2,2,1) with perm(T)= ((1, 2, 5, 4, 3, 7, 9, 8, 6), (10,))

In [5]: g.generators

Out[6]: u'[[0, -1, 1, 0], [4, -1, 9, -2], [-4, 3, -7, 5], [1, -2, 1, -1]]'

Print tables #:

ipython In[1]: import noncong.subgroups.models In[2]: fp=open('table.html','w') In[3]: s=noncong.backend.print_table.print_table_of_groups(index_max=17,format='html') In[4]: fp.writelines(s) In[5]: fp.close() In[2]: fp=open('table.tex','w') In[3]: s=noncong.backend.print_table.print_table_of_groups(index_max=17,format='latex') In[4]: fp.writelines(s) In[5]: fp.close()