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


# 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 = [6,6,0,6,4,0,4,6,0,4,13,0,-3,4,0,6,2,0,26,4,0,13,30,0,10,-3,0,
4,1,0,-3,6,0,2,40,0,12,26,0,4,10,0,0,13,0,30,38,0,40,10,0,-3,-2,0,11,4,
0,1,2,0,3,-3,0,6,-16,0,-9,2,0,40,-16,0,7,12,0,26,-31,0,14,4,0,10,24,0,
-1,0,0,13,-34,0,5,30,0,38,15,0,-9,40,0,10]
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