Re: Question regarding trace map

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

On Tue, Sep 10, 2024 at 03:11:57PM +0000, LNU, Swati wrote:
> Hello,
> Sure, here is my attempt with result. I used this formula to compute trace of f(z).
> Tr_{N/p}^{N}(f) = f + p^{1-k/2} f | W_{N}^{p} | U_{p} and det(W_{N}^{p}) = 2
> For p = 2, we have, Tr_{3}^{6}(f) = f + (2)^{-1}  \sum_{j = 0}^{j = 1} f | [4, 1; 6, 2] | [1, j ; 0, 2]
> 
> Here is the code:
> ............................................................................................................................................
> mf = mffrometaquo([1,2;2,2;3,2;6,2]);
> mf1 = mfinit(mf);
> a = mfcoefs(mf, 100);
> b = (1/2) * (mfslashexpansion(mf1, mf, [4,2;6,4],100,0));
> c = (1/2) * (mfslashexpansion(mf1, mf, [4,6;6,10],100,0));
> d = a + b + c
> 
> Output:
> [0,1,-5/2,-3,5,6,15/2,-16,-10,9,-15,38,40,....]

My guess is that you need to multiply the matrices in the other direction, and omit the 1/2.

a = mfcoefs(mf, 100);
b = mfslashexpansion(mf1, mf, [1, 0 ; 0, 2] * [4, 1; 6, 2],100,0);
c = mfslashexpansion(mf1, mf, [1, 1 ; 0, 2] * [4, 1; 6, 2],100,0);
a+b+c
%49 = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]

Cheers,
Bill.