# SageMath code for working with modular form 3600.2.x.e


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 0, 3]))
N = Newforms(chi, 2, names="a")

# select newform: 
traces = [4,0,0,0,0,0,0,0,0,0,0,0,-4,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,-20,0,0,0,-8,0,0,0,0,0,0,0,0,0,0,0,-28,0,0,0,0,0,0,0,24,0,
0,0,0,0,0,0,0,0,0,0,28,0,0,0,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
28,0,0,0,40]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(101)] == traces)

# q-expansion: 
f.q_expansion() # note that sage often uses an isomorphic number field