Re: Fwd: Q-expansion question

Kevin,

Soon the LMFDB classical modular forms section will be receiving a major upgrade -- several people have been working on this for some months, as I will report in Bordeaux in 2 weeks. The new data has been computed (in most cases) both in Magma and in Pari with checks for consistency. After that upgrade is in place we (LMFDB) will add code snippets as on several other LMFDB pages to enable the objects in question to be constructed in Pari and other systems. Then it will be easy to do the sort of thing you asked about.

Jhn

On Thu, 3 Jan 2019 at 08:55, Kevin Acres <research@research-systems.com> wrote:

Thanks for that, it worked well.

On Sat, December 29, 2018 8:54 am, Karim Belabas wrote:
> * Kevin Acres [2018-12-28 22:33]:
>
>> I’m trying to reproduce with pari/gp the q expansion shown at :
>> http://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/137/2/1/a/
>>
>>
>> I’m using pari/gp 2.12.0 but struggling to get a match.
>>
>>
>> Any ideas?
>>
>
> (22:42) gp > mf = mfinit([137,2], 0);
> (22:43) gp > F = mfeigenbasis(mf); #F
> %2 = 2
> (22:43) gp > nfs = mffields(mf)
> %3 = [y^4 - y^3 - 3*y^2 + y + 1, y^7 - 12*y^5 - 10*y^4 + 24*y^3 + 31*y^2 +
> 11*y + 1]
>
>
> The first one is obviously isomorphic to the a^4 + 3*a^3 − 4*a − 1 = 0 in
> LMFDB:
>
>
> (22:43) gp > nfisisom(nfs[1], a^4 + 3*a^3 - 4*a - 1)
> %4 = [a + 1, a^3 + 2*a^2 - 2*a - 2]
>
>
> (22:43) gp > v = lift(mfcoefs(F[1],10))
> %5 = [0, 1, y - 1, y^3 - 2*y^2 - 2*y + 1, y^2 - 2*y - 1, -2*y^3 + 3*y^2 +
> 3*y - 3, -2*y^3 + 3*y^2 + 2*y - 2, -y^3 + y^2 + 3*y - 4, y^3 - 3*y^2 - y
> + 3, 2*y^2 - y - 2, 3*y^3 - 6*y^2 - 4*y + 5]
>
>
> \\ apply isomorphism (the other one gives a conjugate)
> (22:43) gp > lift(subst(v, 'y, Mod(a + 1, a^4 + 3*a^3 - 4*a - 1)))
> %6 = [0, 1, a, a^3 + a^2 - 3*a - 2, a^2 - 2, -2*a^3 - 3*a^2 + 3*a + 1,
> -2*a^3 - 3*a^2 + 2*a + 1, -a^3 - 2*a^2 + 2*a - 1, a^3 - 4*a, 2*a^2 + 3*a
> - 1, 3*a^3 + 3*a^2 - 7*a - 2]
>
>
> Hope this helps,
>
>
> K.B.
> --
> Karim Belabas, IMB (UMR 5251) Tel: (+33) (0)5 40 00 26 17
> Universite de Bordeaux Fax: (+33) (0)5 40 00 21 23
> 351, cours de la Liberation http://www.math.u-bordeaux.fr/~kbelabas/
> F-33405 Talence (France) http://pari.math.u-bordeaux.fr/ [PARI/GP]
> `
>
>
>