Eigenform formula in S2(K(523))+

(Filename: eig-formula-2-523-1.html)

FORMULA for nonlift eigenform f ∈ S2(K(523))+
The eigenform formula is
    f = 10 Borch(ψ) + Σj=117 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
−15
TB(2;3,3,4,6,6,7,9,12,15,21)
−3
TB(2;3,3,4,6,7,9,10,11,15,20)
1
TB(2;3,3,4,7,7,10,10,13,16,17)
3
TB(2;3,3,4,7,7,10,11,12,15,18)
−20
TB(2;3,3,4,7,8,10,11,11,14,19)
16
TB(2;3,3,5,6,8,9,11,12,14,19)
−2
TB(2;3,4,4,5,7,7,11,12,16,19)
11
TB(2;3,4,4,7,8,8,11,11,15,19)
−17
TB(2;1,1,2,3,4,5,6,7,8,29)
21
TB(2;1,1,2,3,4,5,6,7,11,28)
14
TB(2;1,1,2,3,4,5,7,11,12,26)
13
TB(2;1,1,2,3,4,5,7,13,14,24)
14
TB(2;1,1,2,3,4,6,7,13,19,20)
2
TB(2;3,4,5,6,7,8,11,13,14,19)
1
TB(2;1,1,2,3,5,11,12,14,16,17)
7
TB(2;2,2,4,6,7,8,8,10,15,22)
−18
TB(2;2,2,4,6,10,11,12,13,14,16)

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