# SageMath code for working with modular form 1300.2.d.d


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")

# select newform: 
traces = [6,0,0,0,0,0,0,0,-6,0,0,0,6]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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