# SageMath code for working with modular form 6.18.a.b


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a") 

# select newform: 
traces = [1,-256,6561]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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