L-series attached to cusp forms are broken

[was]

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.

[was]

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]

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

[mneururer]

Review: This patch allows one to compute with L-functions of non-rational new forms and fixes the first problem mentioned in the description (the one ending with 'Boom!' now produces a real number).

[tornaria]

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