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


# 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 = [10,-10,0,10,-5,0,4,-10,0,5,-16,0,17,-4,0,10,-8,0,4,-5,0,16,-21,
0,19,-17,0,4,-3,0,21,-10,0,8,1,0,3,-4,0,5,-19,0,0,-16,0,21,1,0,-2,-19,
0,17,-30,0,-16,-4,0,3,-9,0,-15,-21,0,10,31,0,17,-8,0,-1,-18,0,4,-3,0,4,
-3,0,34,-5,0,19,-16,0,-17,0,0,16,35,0,-40,-21,0,-1,64,0,32,2,0,19]
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