# SageMath code for working with modular form 31680.2.a.dx


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(31680, 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(31680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [1,0,0,0,1,0,4,0,0,0,-1,0,-4,0,0,0,-4,0,-4,0,0,0,6,0,1,0,0,0,
-10,0,-4,0,0,0,4,0,-2,0,0,0,10,0,-8,0,0,0,-6,0,9,0,0,0,2,0,-1,0,0,0,4,
0,10,0,0,0,-4,0,-2,0,0,0,0,0,12,0,0,0,-4,0,-8,0,0,0,0,0,-4,0,0,0,10,0,
-16,0,0,0,-4,0,-2,0,0,0]
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