# SageMath code for working with modular form 33282.2.a.bg


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33282, 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(33282, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [1,1,0,1,3,0,1,1,0,3,1,0,1,1,0,1,-4,0,-1,3,0,1,4,0,4,1,0,1,-9,
0,2,1,0,-4,3,0,-2,-1,0,3,8,0,0,1,0,4,11,0,-6,4,0,1,-4,0,3,1,0,-9,12,0,
0,2,0,1,3,0,2,-4,0,3,12,0,-4,-2,0,-1,1,0,14,3,0,8,-3,0,-12,0,0,1,-10,0,
1,4,0,11,-3,0,17,-6,0,4]
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