# SageMath code for working with modular form 882.4.g.bd


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")

# select newform: 
traces = [4,-4,0,-8,12,0,0,32,0,24,-4,0,96]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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