# SageMath code for working with modular form 15925.2.a.f


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15925, 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(15925, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [1,-1,0,-1,0,0,0,3,-3,0,-3,0,1,0,0,-1,-7,3,-7,0,0,3,6,0,0,-1,
0,0,-5,0,0,-5,0,7,0,3,-8,7,0,0,0,0,-2,3,0,-6,-7,0,0,0,0,-1,3,0,0,0,0,5,
-7,0,-7,0,0,7,0,0,3,7,0,0,-5,-9,-14,8,0,7,0,0,-6,0,9,0,0,0,0,2,0,-9,0,
0,0,-6,0,7,0,0,14,0,9,0]
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