# SageMath code for working with modular form 19663.2.a.o


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(19663, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
B = ModularForms(chi, 1).cuspidal_submodule().basis()
N = [B[i] for i in range(len(B))]

# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(19663, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [39,-3,-3,39,-12,0,-39,-9,42,-6,3,-6,0,3,-3,39,-3,24,9,-72,3,
-30,-6,0,39,12,-78,-39,12,-6,-12,-21,-24,-24,12,-3,-6,18,90,3,-42,0,0,
9,-33,0,-30,57,39,3,-9,-18,0,-36,-60,9,-42,-18,27,150,-3,-75,-42,39,9,
45,-12,45,-42,6,0,39,-75,-141,-66,48,-3,-45,45,-6,147,63,-54,6,-18,-9,
-45,-75,-9,15,0,-108,36,-48,-24,-18,6,-3,3,27]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)

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