# SageMath code for working with modular form 27885.2.a.ec


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27885, 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(27885, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [36,3,36,45,36,3,20,9,36,3,36,45,0,18,36,55,6,3,40,45,20,3,26,
9,36,0,36,58,5,3,34,26,36,38,20,45,46,24,0,9,-1,18,-12,45,36,46,22,55,
68,3,6,0,31,3,36,20,40,27,46,45,2,3,20,35,0,3,79,-25,26,18,28,9,76,-18,
36,68,20,0,22,55,36,-54,34,58,6,30,5,9,34,3,0,42,34,-27,40,26,92,0,36,
45]
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