# SageMath code for working with modular form 930.2.i.n


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
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(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [6,-6,3,6,-3,-3,-4,-6,-3,3,5]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

# q-expansion: 
f.q_expansion() # note that sage often uses an isomorphic number field