# SageMath code for working with modular form 42237.2.a.h


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(42237, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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(42237, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [2,-2,0,2,2,0,2,-6,0,2,0,0,2,6,0,6,4,0,0,-6,0,-8,2,0,-4,-2,0,
-14,8,0,8,6,0,-20,10,0,-6,0,0,-2,4,0,-8,16,0,10,4,0,4,12,0,2,-2,0,-8,2,
0,-16,-14,0,-6,0,0,-14,2,0,-24,36,0,2,14,0,4,-2,0,0,-16,0,10,6,0,20,8,
0,-12,0,0,-8,-24,0,2,-22,0,-4,0,0,-18,12,0,-20]
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