# SageMath code for working with modular form 30345.2.a.ea


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(30345, 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(30345, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [24,3,24,27,-24,3,-24,12,24,-3,-9,27,6,-3,-24,33,0,3,12,-27,-24,
-15,-6,12,24,6,24,-27,18,-3,9,27,-9,0,24,27,0,24,6,-12,33,-3,18,-18,-24,
-48,21,33,24,3,0,45,12,3,9,-12,12,-39,18,-27,-6,24,-24,30,-6,-15,24,0,
-6,3,12,12,-6,-12,24,24,9,6,12,-33,24,-42,6,-27,0,30,18,39,63,-3,-6,-18,
9,12,-12,27,-3,3,-9,27]
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