# SageMath code for working with modular form 22848.2.a.fn


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(22848, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")

# select newform: 
traces = [4,0,4,0,5,0,4,0,4,0,-1,0,-1,0,5,0,4,0,7,0,4,0,13,0,7,0,4,0,0,
0,18,0,-1,0,5,0,10,0,-1,0,11,0,-1,0,5,0,-2,0,4,0,4,0,-2,0,-3,0,7,0,6,0,
6,0,4,0,7,0,0,0,13,0,16,0,-10,0,7,0,-1,0,4,0,4,0,-2,0,5,0,0,0,2,0,-1,0,
18,0,17,0,-10,0,-1,0]
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