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


# 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 = [6,0,0,6,-9,0,9,-3,0,-6,-9,0,-3,-6,0,6,-15,0,0,9,0,21,-6,0,15,
0,0,-3,-15,0,0,-21,0,-33,3,0,6,0,0,-39,6,0,15,6,0,27,-9,0,9,-9,0,-18,-6,
0,-6,-39,0,-12,-15,0,3,-27,0,21,-21,0,18,-21,0,-9,-15,0,-6,-9,0,0,-48,
0,-21,21,0,-15,3,0,42,-30,0,42,-24,0,-12]
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