Eigenform formula in S2(K(389))+

(Filename: eig-formula-2-389-1.html)

FORMULA for nonlift eigenform f ∈ S2(K(389))+
The eigenform formula is
    f = 10 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
−3
TB(2;1,1,1,2,3,4,5,6,18,19)
−2
TB(2;2,2,3,4,5,6,8,10,14,18)
6
TB(2;1,1,2,2,3,5,12,13,14,15)
−11
TB(2;2,2,5,6,7,8,9,11,13,15)
5
TB(2;2,2,5,6,7,9,9,11,11,16)
7
TB(2;1,1,2,3,3,5,6,12,15,18)
16
TB(2;1,1,2,3,4,5,6,7,14,21)
3
TB(2;1,1,2,3,6,8,9,10,11,19)
−2
TB(2;2,3,3,5,5,7,8,10,13,18)
−2
TB(2;1,1,2,6,9,10,11,11,12,13)
7
TB(2;1,1,3,4,5,6,8,9,16,17)

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