Eigenform formula in S2(K(349))+

(Filename: eig-formula-2-349-1.html)

FORMULA for nonlift eigenform f ∈ S2(K(349))+
The eigenform formula is
    f = 13 Borch(ψ) + Σj=111 cj Grit(φj)
where ψ can be found here or here, and where the coefficients cj and theta blocks φj are given as follows.
cjφj
7
TB(2;2,2,2,4,5,7,9,11,13,15)
1
TB(2;1,1,1,2,5,6,11,12,13,14)
5
TB(2;1,1,1,2,6,7,8,9,10,19)
1
TB(2;2,2,3,5,5,7,7,10,12,17)
−3
TB(2;2,2,3,5,5,8,9,11,13,14)
−4
TB(2;1,1,2,2,3,5,7,8,10,21)
−2
TB(2;1,1,2,2,3,5,9,11,14,16)
4
TB(2;1,1,2,2,7,9,9,10,11,16)
1
TB(2;1,1,2,3,4,5,6,7,14,19)
2
TB(2;1,1,2,3,4,5,6,11,14,17)
−2
TB(2;2,3,5,5,6,7,9,10,12,15)

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