# SageMath code for working with modular form 3249.2.a.b


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3249, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [1,-2,0,2,3,0,-5,0,0,-6,-1,0,-2,10,0,-4,1,0,0,6,0,2,4,0,4,4,0,
-10,-2,0,6,8,0,-2,-15,0,0,0,0,0,0,0,-1,-2,0,-8,9,0,18,-8,0,-4,10,0,-3,
0,0,4,-8,0,-1,-12,0,-8,-6,0,-8,2,0,30,-12,0,-11,0,0,0,5,0,-16,-12,0,0,
-12,0,3,2,0,0,-6,0,10]
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