# SageMath code for working with modular form 45570.2.a.hu


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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(45570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [14,-14,14,14,14,-14,0,-14,14,-14,4,14,2,0,14,14,-2,-14,2,14,
0,-4,4,-14,14,-2,14,0,4,-14,-14,-14,4,2,0,14,-24,-2,2,-14,-18,0,-24,4,
14,-4,-20,14,0,-14,-2,2,-22,-14,4,0,2,-4,-24,14,-4,14,0,14,2,-4,-50,-2,
4,0,16,-14,-16,24,14,2,0,-2,-12,14,14,18,-12,0,-2,24,4,-4,-28,-14,0,4,
-14,20,2,-14,-34,0,4,14]
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