# SageMath code for working with modular form 33600.2.a.jy


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")

# select newform: 
traces = [3,0,-3,0,0,0,3,0,3,0,2,0,2,0,0,0,0,0,2,0,-3,0,8,0,0,0,-3,0,-2,
0,2,0,-2,0,0,0,-4,0,-2,0,14,0,-12,0,0,0,8,0,3,0,0,0,14,0,0,0,-2,0,8,0,
-2,0,3,0,0,0,0,0,-8,0,6,0,-6,0,0,0,2,0,20,0,3,0,-8,0,0,0,2,0,2,0,2,0,-2,
0,0,0,14,0,2,0]
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