On Sun, Feb 14, 2016 at 6:55 AM, Misja <[email protected]> wrote:
> In Magma there exists a Reductions(f,p) command, which for any modular form
> f defined over a number field K and a prime P, outputs all the ''f mod P''
> reductions for primes P of O_K s.t. P|p.
I implemented that in Magma. I never got around to implementing in
Sage. Here's a straightforward implementation:
def modp_reductions(f, p, prec=None):
K = f.base_ring()
g = f.q_expansion(prec)
return [g.change_ring(P.residue_field()) for P, e in K.factor(p)]
For example,
f = CuspForms(23).newforms('a')[0]
modp_reductions(f, 5)
modp_reductions(f, 7)
modp_reductions(f, 11)
If you're trying to push the limits of research, there may be ways to
make this much faster (by working only with a p-maximal order)... but
for some applications the above should be fine.
See
https://cloud.sagemath.com/projects/4a5f0542-5873-4eed-a85c-a18c706e8bcd/files/support/2016-02-14-modp-modform.sagews
>
> For the Magma function see:
> https://magma.maths.usyd.edu.au/magma/handbook/text/1552#17206
>
> Does anyone know if a similar function exists in SAGE? It seems like
> something I would expect to exist in SAGE, but I have not been able to find
> it.
>
> Thanks.
>
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William (http://wstein.org)
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