# SageMath code for working with modular form 20070.2.a.e


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20070, 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(20070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [1,-1,0,1,-1,0,0,-1,0,1,-1,0,4,0,0,1,5,0,-1,-1,0,1,5,0,1,-4,0,
0,-3,0,2,-1,0,-5,0,0,-9,1,0,1,-4,0,-12,-1,0,-5,0,0,-7,-1,0,4,12,0,1,0,
0,3,1,0,13,-2,0,1,-4,0,-15,5,0,0,14,0,-14,9,0,-1,0,0,-3,-1,0,4,4,0,-5,
12,0,1,8,0,0,5,0,0,1,0,2,7,0,1]
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