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


# 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 = [1,-1,0,-1,1,0,-2,3,0,-1,6,0,0,2,0,-1,6,0,0,-1,0,-6,8,0,1,0,0,
2,4,0,0,-5,0,-6,-2,0,-4,0,0,3,0,0,-2,-6,0,-8,8,0,-3,-1,0,0,2,0,6,-6,0,
-4,12,0,2,0,0,7,0,0,8,-6,0,2,16,0,14,4,0,0,-12,0,-8,-1,0,0,0,0,6,2,0,18,
0,0,0,-8,0,-8,0,0,12,3,0,-1]
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