# SageMath code for working with modular form 28050.2.a.cy


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(28050, 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(28050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [1,1,1,1,0,1,-4,1,1,0,1,1,-6,-4,0,1,1,1,4,0,-4,1,0,1,0,-6,1,-4,
2,0,0,1,1,1,0,1,10,4,-6,0,-10,-4,4,1,0,0,-4,1,9,0,1,-6,2,1,0,-4,4,2,0,
0,2,0,-4,1,0,1,-12,1,0,0,0,1,10,10,0,4,-4,-6,4,0,1,-10,12,-4,0,4,2,1,-14,
0,24,0,0,-4,0,1,-18,9,1,0]
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