# SageMath code for working with modular form 9747.2.a.bd


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9747, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")

# select newform: 
traces = [3,3,0,3,3,0,-9,6,0,0,9,0,-9,-12,0,3,3,0,0,3,0,18,-3,0,-6,-12,
0,-18,6,0,0,0,0,-9,-12,0,-27,0,0,18,21,0,-18,18,0,-9,6,0,12,-15,0,-9,6,
0,0,-33,0,-9,3,0,-9,-3,0,12,-3,0,-9,-33,0,-9,3,0,-18,-21,0,0,-27,0,0,12,
0,18,0,0,-9,-3,0,9,33,0,24]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(91)] == traces)

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