# SageMath code for working with modular form 325.3.t.a


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 3, names="a")

# select newform: 
traces = [4,2,2,-6,0,10,-16,6]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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