# SageMath code for working with modular form 7056.2.h.k


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7056, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")

# select newform: 
traces = [8,0,0,0,0,0,0,0,0,0,0,0,-16,0,0,0,0,0,0,0,0,0,0,0,-24,0,0,0,
0,0,0,0,0,0,0,0,-32,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,-32,0,0,0,0,0,0,0,0,0,0]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(83)] == traces)

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