# SageMath code for working with modular form 17550.2.a.ee


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17550, 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(17550, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [3,-3,0,3,0,0,-2,-3,0,0,2,0,3,2,0,3,0,0,-8,0,0,-2,2,0,0,-3,0,
-2,-10,0,-2,-3,0,0,0,0,-7,8,0,0,2,0,8,2,0,-2,12,0,-9,0,0,3,15,0,0,2,0,
10,8,0,-24,2,0,3,0,0,1,0,0,0,9,0,16,7,0,-8,20,0,-7,0,0,-2,8,0,0,-8,0,-2,
-17,0,-2,2,0,-12,0,0,2,9,0,0]
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