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


# 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 = [90,-5,1,97,4,5,90,-12,123,7,42,4,17,-5,67,103,53,-21,7,18,1,
19,10,1,122,20,-29,97,97,-165,21,-19,14,-9,4,142,40,39,19,-9,18,5,23,78,
59,12,49,23,90,-9,-16,19,0,35,20,-12,153,-77,35,195,-35,93,123,96,40,-39,
-113,176,27,7,35,-9,9,32,7,57,42,72,28,-71,290,68,-42,4,77,-12,27,75,127,
24,17,25,92,38,153,-48,46,-5,127,96]
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