#6837: Implementation of twisting modular forms by Dirichlet characters
-------------------------------------+-------------------------------------
Reporter: ljpk | Owner: craigcitro
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-6.4
Component: modular forms | Resolution:
Keywords: modular form | Merged in:
twist character | Reviewers:
Authors: Lloyd Kilford, | Work issues:
Alex Ghitza, Peter Bruin | Commit:
Report Upstream: N/A | e576ad46ca1427fde0e570371d1c5ef670a863ed
Branch: | Stopgaps:
u/pbruin/6837-modular_form_twist |
Dependencies: |
-------------------------------------+-------------------------------------
Changes (by wuthrich):
* status: needs_review => needs_work
Comment:
I tested this and all test passed. However, I am not sure about the
implementation. There is only one (rather trivial) test in the
documentations. So I played around a bit.
Currently it fails if the form is a {{{NewForm}}} as explained in #18086
.
It also fails if f does not have a neben character:
{{{
sage: M = CuspForms(Gamma1(13),4)
sage: f = M.basis()[13]
sage: G = DirichletGroup(11)
sage: chi = G.0
sage: f.twist(chi)
}}}
gives {{{ValueError: Form is not an eigenvector for <2>}}}
Similarly it fails when the character has values outside the field of
coefficients of f:
{{{
sage: M = CuspForms(Gamma0(37),2)
sage: f = M.0
sage: G = DirichletGroup(11)
sage: chi = G.0
sage: chi
Dirichlet character modulo 11 of conductor 11 mapping 2 |--> zeta10
sage: f.twist(chi)
}}}
returns {{{ValueError: No coercion defined}}}.
Now some of these problems may be due to user choosing bad input. But that
should be checked in the function or (at the least) be documented. Alas, I
revert it to needs work.
However I do thank you for picking up this old ticket and working on it. I
really would like to see this work in Sage. Thanks for picking up on David
Loeffler's comments.
--
Ticket URL: <http://trac.sagemath.org/ticket/6837#comment:20>
Sage <http://www.sagemath.org>
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