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


# 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 = [2,2,0,-2,2,0,-2,-6,0,2,-2,0,-2,-2,0,-2,4,0,0,-2,0,-2,4,0,2,-2,
0,2,-6,0,4,10,0,4,-2,0,-6,0,0,-6,10,0,-14,2,0,4,-12,0,22,2,0,2,8,0,-2,
6,0,-6,8,0,8,4,0,14,-2,0,4,-4,0,-2,-12,0,0,-6,0,0,-32,0,-8,-2,0,10,-8,
0,4,-14,0,6,26,0,36,-4,0,-12,0,0,-2,22,0,-2]
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