# SageMath code for working with modular form 38646.2.a.p


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38646, 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(38646, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [1,1,0,1,-4,0,-4,1,0,-4,0,0,0,-4,0,1,6,0,1,-4,0,0,-6,0,11,0,0,
-4,6,0,10,1,0,6,16,0,-12,1,0,-4,-10,0,-4,0,0,-6,6,0,9,11,0,0,-2,0,0,-4,
0,6,12,0,6,10,0,1,0,0,-8,6,0,16,0,0,-10,-12,0,1,0,0,10,-4,0,-10,-12,0,
-24,-4,0,0,-6,0,0,-6,0,6,-4,0,6,9,0,11]
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