Question regarding trace map

["LNU, Swati" <S10@email.sc.edu>]

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]).

This doesn't evaluate to 0. Can someone please suggest what am I doing wrong.

Thanks,

Swati

"The pursuit of science is at its best when it is a part of a way of life" - Alladi Ramakrishnan.