# SageMath code for working with modular form 7200.2.b.c


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")

# select newform: 
traces = [4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,32,0,0,0,0,0,-20,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,-16]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(67)] == traces)

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