Re: Question regarding trace map

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

On Mon, Sep 09, 2024 at 08:33:46PM +0000, LNU, Swati wrote:
> Hi all,
> I am trying to show using pari/gp  that trace map of f(z) = eta(z)^2 * eta(2z)^2  * eta(3z)^2  * eta(6z)^2 is 0.
> I am using this defn. of trace map.
> Tr_{N/p}^{N}(f) = f + p^{1 - (k/2)}  f | W_{N}^{p} | U_{p} where W_{N}^{p} = [pa, 1; Nb, p] with det(W_{N}^{p}) = p and
> f | U_{p} = \sum_{j = 0}^{p-1} f | [1, j ; 0, p]
> Taking N = 6, k = 4, p = 2, W_{6}^{2} = [4, 1; 6, 2], the computation reduces to the following:
> 
 Ser(mfcoefs(mffrometaquo([1, 2; 2, 2; 3, 2; 6, 2], 100), q) + (1/2) *
 Ser(mfslashexpansion(mf, f, [4, 2; 6, 4], 100, 0), q) + (1/2) *
 Ser(mfslashexpansion(mf, f, [4, 6; 6, 10], 100, 0), q) 
> where mf is the space
> where f belongs to and f = mffrometaquo([1, 2; 2, 2; 3, 2; 6, 2]).

You do not need to use Ser, you can add the vectors directly.
Furthermore, you are missing some parenthesis.

Cheers,
Bill.