# SageMath code for working with modular form 3200.1.bd.b


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3200, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 5, 2]))
N = Newforms(chi, 1, names="a")

# select newform: 
f = N[0] # Warning: the index may be different

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