Re: Finding the generating funcction for a theta sequence?

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

On Sun, Nov 24, 2019 at 05:03:42PM +0100, Karim Belabas wrote:
> * Karim Belabas [2019-11-24 16:51]:
> [...]
> > So you can actually write it only in terms of F_2 (= mfeisenstein(2)). More
> > precisely
> > 
> > (-12 B(2) + 152 B(4) + 36 B(6) - 2176 B(8) + 3640 B(12) - 1664 B(24)) . F_2
> > 
> > (where B(n) is the q -> q^n operator). In fact, from this description, your
> > original form had level 12:
> [...]
> 
> Sorry, this doesn't work out numerically. Which means (unless I goofed again),
> that your F doesn't belong to the modular form space we assigned to it,
> hence is not a modular form (i.e. it has poles).

Indeed.

? L=mflinear(mf,mftobasis(mf,F));
? mfcoefs(L,100)
%17 =
[1,0,-12,0,116,0,-12,0,-1804,0,-72,0,4212,0,-96,0,-5644,0,-12,0,696,0,-144,0,2292,0,-168,0,928,0,-72,0,-13324,0,-216,0,16500,0,-240,0,-10824,0,-96,0,1392,0,-288,0,-1548,0,-372,0,1624,0,-12,0,-14432,0,-360,0,25272,0,-384,0,-28684,0,-144,0,2088,0,-576,0,14580,0,-456,0,2320,0,-168,0,-33864,0,-504,0,33696,0,-528,0,-21648,0,-72,0,2784,0,-576,0,-9228,0,-684,0,3596]

this is not what we are looking for.

Cheers,
Bill