# SageMath code for working with modular form 10816.2.a.bk


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10816, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")

# select newform: 
traces = [1,0,3,0,-3,0,1,0,6,0,4,0,0,0,-9,0,5,0,6,0,3,0,6,0,4,0,9,0,4,
0,0,0,12,0,-3,0,-3,0,0,0,-12,0,-3,0,-18,0,-7,0,-6,0,15,0,2,0,-12,0,18,
0,-2,0,12,0,6,0,0,0,4,0,18,0,11,0,-6,0,12,0,4,0,6,0,9,0,10,0,-15,0,12,
0,-6,0,0,0,0,0,-18,0,0,0,24,0]
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