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


# 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 = [20,20,0,20,6,0,-20,20,0,6,2,0,-2,-20,0,20,-8,0,-28,6,0,2,0,0,
24,-2,0,-20,24,0,-14,20,0,-8,-30,0,-42,-28,0,6,-30,0,0,2,0,0,28,0,30,24,
0,-2,-8,0,-48,-20,0,24,-28,0,8,-14,0,20,-36,0,4,-8,0,-30,38,0,-92,-42,
0,-28,2,0,8,6,0,-30,-30,0,-52,0,0,2,-20,0,-38,0,0,28,74,0,-34,30,0,24]
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