L-series attached to cusp forms are broken

[williamstein]

sage: C = CuspForms(43,2)
sage: N = C.newforms('a')
sage: f = N[1]
sage: L = f.cuspform_lseries()
Boom!

There are two issues:

(1) the code doesn't work at all when the degree of the form is > 1, which is the main interesting case,

(2) the name "cuspform_lseries" is bad, since f is already a cuspform, and we use the name "lseries" in all other places (e.g., elliptic curves, abelian varieties), so it is hard to find. In fact, I didn't even think to look for cuspform_lseries, instead only finding this via lots of grepping and reading source code.

So to fix this issue, I think (1) the bug should get fixed, and (2) the name should be changed (actually deprecate the old name as explained in the developers guide and introduce the name lseries).

See also #12015.

The part about deprecating cuspform_lseries() is moved to #16917.

Depends on #16916

Component: number theory

Author: Gonzalo Tornaría

Branch/Commit: 1939a9c

Reviewer: Michael Neururer

Issue created by migration from https://trac.sagemath.org/ticket/11631

[williamstein]

comment:1

I have now written (or am writing) similar (but more powerful) functionality for psage. It'll end up in this directory of psage: psage/lseries/

http://code.google.com/p/purplesage/source/browse/#hg%2Fpsage%2Flseries

[tornaria]

Branch: u/tornaria/11631

[tornaria]

comment:7

Inspired in the patch at #12015, I added a parameter to cuspform_lseries() so one can specify which of the conjugates of the newform to use (defaults to 0). The order is arbitrary as it comes from the embeddings() method for self.base_ring().

In the long term #12015 is much more general, but this is a good fix and much easier to review and merge.

---

New commits:

74b6a67	Trac #16916: fix precision issues in cuspform_lseries()
ae26b4a	Trac #16916: avoid precision issues in cuspform_lseries
13dbf33	remove tabs
1939a9c	Trac #11631: fix cuspform_lseries() for non-rational newforms

[tornaria]

Author: tornaria

[tornaria]

Commit: 1939a9c

[tornaria]

Dependencies: #16916

[sagetrac-mneururer]

comment:9

Review: This patch allows one to compute with L-functions of non-rational new forms and fixes the problem in the description.

[sagetrac-mneururer]

Reviewer: Michael Neururer

[tornaria]

comment:11

I moved the part about deprecation to #16917 so the bugfix can be reviewed and merged independently.

[tornaria]

Changed author from tornaria to Gonzalo Tornaría

[vbraun]

Changed branch from u/tornaria/11631 to 1939a9c