Kevin Acres on Sat, 23 Nov 2019 12:52:01 +0100

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 Re: Finding the generating funcction for a theta sequence?

```Hi Karim,

Thanks for the pointer. A longer sequence is:
[1, -12, 116, -12, -1804, 8120, 116, -155744, 684532, -12, -13237576,
58212208, -1804, -1125531816, 4949148576, 8120, -95692200972,
420774756136, 116, -8135721271536, 35774143649208, -155744,
-691696548706960, 3041506787016416, 684532, -58807829742387572,
258587980022941272, -12];

But I didn't get a match on that.

It's basically newform 24.6.a.b divided by 24.4.a.a (From LMFDB).

Regards,

Kevin.

On Sat, November 23, 2019 10:34 pm, Karim Belabas wrote:
> * Kevin Acres [2019-11-23 12:11]:
>
>> I have sequence:
>>
>>
>> [1, -12, 116, -12, -1804, 8120, 116, -155744, 684532, -12]
>>
>>
>> that has a couple of siblings:
>>
>> OEIS A186100
>> [1, -12, -12, -12, -12, -72, -12, -96, -12, -12, -72, -144]
>>
>>
>> and OEIS A125510
>> [1, 6, 6, 42, 6, 36, 42, 48, 6, 150, 36, 72]
>>
>>
>> I strongly suspect my sequence to also be a theta series, which raises
>> my question - is there a way to try and derive it's generating function
>> using pari/gp?
>
> No direct support for this, but you can try to recognize them as modular
> forms:
>
>
> ? m = [1, -12, 116, -12, -1804, 8120, 116, -155744, 684532, -12];
> ? L = mfsearch([[1..30], 2], m);
> ? [ print(mfcoefs(f, 11)) | f <- L ];
> [1, -12, 116, -12, -1804, 8120, 116, -155744, 684532, -12, 672816, 856096]
>  \\ single solution in level <= 30 and weight 2.
>
>
> You may have to input more terms: there are 336 solutions in level <= 300
> ...
> (31 of which have integer coefficients)
>
>
> Once you identify the form, in particular its level, you can look for
> theta series in the corresponding modular form space [using, e.g.,
> mffromqf and/or a database of lattices]
>
> Cheers,
>
>
> 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]
> `
>
>

```