# SageMath code for working with modular form 25350.2.a.q


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25350, 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(25350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [1,-1,-1,1,0,1,2,-1,1,0,-6,-1,0,-2,0,1,3,-1,-2,0,-2,6,6,1,0,0,
-1,2,3,0,4,-1,6,-3,0,1,-7,2,0,0,3,2,10,-6,0,-6,6,-1,-3,0,-3,0,-3,1,0,-2,
2,-3,0,0,-7,-4,2,1,0,-6,-10,3,-6,0,-6,-1,-13,7,0,-2,-12,0,-4,0,1,-3,-6,
-2,0,-10,-3,6,-18,0,0,6,-4,-6,0,1,14,3,-6,0]
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