Re: parsing pari output for mfgaloistype in weight 1

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Tue, Feb 02, 2021 at 07:24:03PM -0500, Kannappan Sampath wrote:
> Hello everyone:
> 
> I wanted to search for weight 1 forms with a list of properties related to
> its level and conductor of its nebentypus. I have a question I'd like some
> help on. Thank you in advance for your help.
> 
> Let's set
> 
> mfall = mfinit([N, 1, 0], 0);
> 
> Occasionally, the mfgaloistype(mfall[jj]) returns a list of length more
> than 1. I understood this to mean that forms with the given nebentypus have
> projective images as indicated by this list...  but that seems not to match
> with other databases containing similar data (most notably, lmfdb).
> 
> Let me illustrate all this in a particular example I am looking at.
> 
> ? default(parisize, 100000000);
>   ***   Warning: new stack size = 100000000 (95.367 Mbytes).
> ? mfall = mfinit([756, 1, 0], 0);
> ? mfgaloistype(mfall[1])
> % [6, 12]

Dear Kannappan,
This seems like a bug in PARI 2.11, please upgrade to PARI 2.13.1.

On my computer:
? mfall = mfinit([756, 1, 0], 0);
? mfgaloistype(mfall[1])
%2 = [12,12]

If you want to match it with the lmfdb, you should use
mfparams(mfall[1])
to find the corresponding character.

Cheers,
Bill