# SageMath code for working with modular form 3249.2.a.x


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3249, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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(3249, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [3,0,0,0,3,0,-3,3,0,-6,3,0,-3,-6,0,-6,9,0,0,-3,0,-3,-6,0,-6,12,
0,-3,9,0,-24,-9,0,15,3,0,-6,0,0,9,-6,0,-21,12,0,-9,3,0,-12,-9,0,6,-18,
0,6,3,0,-12,-15,0,-9,3,0,-3,-15,0,6,3,0,3,-9,0,-6,3,0,0,0,0,-9,-3,0,21,
15,0,-6,-18,0,6,0,0,-9]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(91)] == traces)

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