# SageMath code for working with modular form 16245.2.a.be


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16245, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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(16245, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [3,-1,0,7,3,0,2,6,0,-1,5,0,-15,-7,0,3,-1,0,0,7,0,-8,-4,0,3,5,
0,11,2,0,-1,6,0,-25,2,0,-2,0,0,6,2,0,-1,18,0,-24,-6,0,-7,-1,0,-35,-11,
0,5,-15,0,-7,-6,0,-9,13,0,-8,-15,0,-20,-34,0,-7,29,0,-22,7,0,0,16,0,-24,
3,0,31,3,0,-1,32,0,-9,14,0,-10,-41,0,21,0,0,7,-23,0,7]
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