# SageMath code for working with modular form 35131.2.a.e


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35131, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")

# select newform: 
traces = [1,1,-2,-1,2,-2,-3,-3,1,2,3,2,-2,-3,-4,-1,-3,1,-1,-2,6,3,-1,6,
-1,-2,4,3,0,-4,2,5,-6,-3,-6,-1,0,-1,4,-6,2,6,0,-3,2,-1,-8,2,2,-1,6,2,4,
4,6,9,2,0,0,4,-13,2,-3,7,-4,-6,6,3,2,-6,8,-3,2,0,2,1,-9,4,10,-2,-11,2,
-15,-6,-6,0,0,-9,2,2,6,1,-4,-8,-2,-10,16,2,3,1]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)

# q-expansion: 
f.q_expansion() # note that sage often uses an isomorphic number field