# SageMath code for working with modular form 9350.2.a.bw


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")

# select newform: 
traces = [3,-3,-3,3,0,3,-7,-3,4,0,-3]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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