# SageMath code for working with modular form 729.2.e.s


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([8]))
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(729, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [12,3,0,-3,-12,0,-3,6,0,-6,3,0,6,6,0,27,-9,0,-12]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

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