# SageMath code for working with modular form 1000.2.bd.a


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1000, base_ring=CyclotomicField(50))
chi = DirichletCharacter(H, H._module([0, 25, 31]))
N = Newforms(chi, 2, 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