#18086: Twists of newforms
-------------------------------------+-------------------------------------
Reporter: pbruin | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.6
Component: modular forms | Resolution:
Keywords: twist newform | Merged in:
Dirichlet character | Reviewers: Chris Wuthrich
Authors: Peter Bruin | Work issues:
Report Upstream: N/A | Commit:
Branch: | dd977f21a88f86e7ecc7712c1b921a23340f6879
u/pbruin/18086-Newform_twist | Stopgaps:
Dependencies: #6837, #18436 |
-------------------------------------+-------------------------------------
Changes (by pbruin):
* dependencies: #6837 => #6837, #18436
Comment:
Replying to [comment:9 wuthrich]:
> Two issues. One a very small missing second ` after check in the
docstring.
Done, thanks,
> The other will need more work:
>
> {{{
> sage: M = CuspForms(Gamma1(13),2)
> sage: f = M.newforms('a')[0]
> sage: G = DirichletGroup(3)
> sage: chi = G.0
> sage: f.twist(chi)
> }}}
> returns
> {{{
> TypeError: no common canonical parent for objects with parents: 'Number
Field in a0 with defining polynomial x^2 + 3*x + 3' and 'Cyclotomic Field
of order 2 and degree 1'
> }}}
>
> It appears when the form has coefficients outside ZZ.
This is because the field of values of `chi` and the field of coefficients
of `f` are not compatible (this may be a bad example; `chi.base_ring()` is
`CyclotomicField(2)`, which is actually `QQ` but not recognised as such).
In such cases, one could try to take a compositum, but I think it is
better to leave it to the user to specify the correct field.
I added youe example, but with `chi` having coefficients in `QQ`.
Unfortunately, this uncovered a new bug; see #18436.
> By the way, this could be another nice example.
> {{{
> sage: D = Newforms(1,12)[0]
> sage: G = DirichletGroup(3)
> sage: chi = G.0
> sage: D.twist(chi)
> }}}
This is actually the first doctest in a different guise. I added another
one to check that twisting by the trivial character (with values in `QQ`)
does not change the form.
--
Ticket URL: <http://trac.sagemath.org/ticket/18086#comment:11>
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