# SageMath code for working with modular form 45760.2.a.gz


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45760, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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(45760, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [16,0,3,0,-16,0,-9,0,21,0,16,0,-16,0,-3,0,-4,0,16,0,1,0,-28,0,
16,0,9,0,1,0,-13,0,3,0,9,0,-12,0,-3,0,3,0,17,0,-21,0,-25,0,17,0,21,0,1,
0,-16,0,-5,0,10,0,-19,0,-22,0,16,0,15,0,-18,0,-3,0,-28,0,3,0,-9,0,-16,
0,20,0,12,0,4,0,-25,0,13,0,9,0,-3,0,-16,0,7,0,21,0]
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