# SageMath code for working with modular form 32490.2.a.cf


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32490, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
B = ModularForms(chi, 1).cuspidal_submodule().basis()
N = [B[i] for i in range(len(B))]

# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32490, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [2,-2,0,2,-2,0,-2,-2,0,2,1,0,1,2,0,2,0,0,0,-2,0,-1,-1,0,2,-1,
0,-2,-12,0,3,-2,0,0,2,0,2,0,0,2,1,0,9,1,0,1,0,0,-12,-2,0,1,11,0,-1,2,0,
12,-10,0,-3,-3,0,2,-1,0,13,0,0,-2,2,0,-15,-2,0,0,-1,0,5,-2,0,-1,-12,0,
0,-9,0,-1,9,0,-1,-1,0,0,0,0,20,12,0,2]
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