# SageMath code for working with modular form 25410.2.a.s


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25410, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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(25410, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [1,-1,-1,1,1,1,1,-1,1,-1,0,-1,2,-1,-1,1,2,-1,2,1,-1,0,-4,1,1,
-2,-1,1,-2,1,-4,-1,0,-2,1,1,8,-2,-2,-1,-6,1,-12,0,1,4,-2,-1,1,-1,-2,2,
4,1,0,-1,-2,2,-12,-1,12,4,1,1,2,0,2,2,4,-1,8,-1,14,-8,-1,2,0,2,-2,1,1,
6,-8,-1,2,12,2,0,6,-1,2,-4,4,2,2,1,-8,-1,0,1]
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