#11215: Various Pairings for Modular Forms
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Reporter: tdupu | Owner: craigcitro
Type: enhancement | Status: new
Priority: minor | Milestone:
Component: modular forms | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Dependencies:
Stopgaps: |
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Old description:
> We should have a functions/functions which allow for pairing of the
> following
>
> -cuspidal modular symbols for Gamma0(N) with cusp forms for Gamma0(N)
>
> -cusp forms for Gamma0(N) with cusp forms Gamma0(N) (petersson inner
> product)
>
> -group elements of Gamma0(N) with cusp forms for Gamma0(N)
>
> Once this is done what works for cusp forms should be extended to
> Meromorphic Differentials of the second kind.
> They should be implemented so that things like
> {{{
> sage: f = CuspForm(15,2).basis()[0]
> sage: g = Gamma0(15).random_element()
> sage: f.pair(g)
> --some number--
> }}}
> should work. Observe that Gamma0(15).random_element() is not implemented.
> A reference for this is chapter 2 of Cremona.
>
> I'm going to attach some code which doesn't work very well and can be
> improved by looking at Fricke involutions but at least it's a start.
> Maybe some people already have some code for this???
New description:
We should have a functions/functions which allow for pairing of the
following
-cuspidal modular symbols for Gamma0(N) with cusp forms for Gamma0(N)
-cusp forms for Gamma0(N) with cusp forms Gamma0(N) (petersson inner
product)
-group elements of Gamma0(N) with cusp forms for Gamma0(N)
Once this is done what works for cusp forms should be extended to
Meromorphic Differentials of the second kind.
They should be implemented so that things like
{{{
sage: f = CuspForm(15,2).basis()[0]
sage: g = Gamma0(15).random_element()
sage: f.pair(g)
--some number--
}}}
should work. Observe that Gamma0(15).random_element() is not implemented.
A reference for this is chapter 2 of Cremona.
I'm going to attach some code which doesn't work very well and can be
improved by looking at Fricke involutions but at least it's a start. Maybe
some people already have some code for this???
Apply [attachment:trac_11215_pairing_redone.patch]
--
Comment (by chapoton):
here is a clean version of the previous patch
for the bot: apply only trac_11215_pairing_redone.patch
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Ticket URL: <http://trac.sagemath.org/ticket/11215#comment:2>
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