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


# 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 = [4,4,4,4,-4,4,-4,4,4,-4,0,4,-1,-4,-4,4,-5,4,-2,-4,-4,0,2,4,4,
-1,4,-4,-15,-4,7,4,0,-5,4,4,-5,-2,-1,-4,-3,-4,-5,0,-4,2,1,4,4,4,-5,-1,
17,4,0,-4,-2,-15,-1,-4,-33,7,-4,4,1,0,7,-5,2,4,-5,4,-21,-5,4,-2,0,-1,-2,
-4,4,-3,-8,-4,5,-5,-15,0,-27,-4,1,2,7,1,2,4,5,4,0,4]
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