Eigenform formula in S2(K(353))+

(Filename: eig-formula-2-353-1.html)

FORMULA for nonlift eigenform f ∈ S2(K(353))+
The eigenform formula is
    f = -11 Borch(ψ) + Σj=111 cj Grit(φj)
where ψ can be found here or here or here, and where the coefficients cj and theta blocks φj are given as follows.
cjφj
2
TB(2;3,3,4,4,5,7,7,10,12,17)
1
TB(2;3,4,4,4,6,7,8,10,12,16)
−2
TB(2;2,2,3,4,5,5,7,9,13,18)
4
TB(2;2,2,3,4,5,6,7,9,11,19)
2
TB(2;2,2,3,4,5,8,10,12,12,14)
0
TB(2;2,2,3,4,6,7,8,10,10,18)
−6
TB(2;2,2,3,5,7,9,10,11,12,13)
−7
TB(2;2,2,4,4,6,6,7,10,11,18)
0
TB(2;2,2,4,5,6,6,8,10,14,15)
−5
TB(2;1,1,2,3,3,4,4,5,7,24)
−1
TB(2;1,1,2,3,4,6,7,13,14,15)

COEFFICIENTS OF f
See here for some Fourier coefficients. Caution: The "unreduced form" data in this other webpage are in the form m, r, n, where the coefficient matrix is half of
 
n r
r m