# SageMath code for working with modular form 240.9.c.a


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 9, names="a")

# select newform: 
traces = [1,0,-81,0,625,0,0,0,6561]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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