# SageMath code for working with modular form 1040.6.a.v # Compute space of new eigenforms: from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1040, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 6, names="a") # select newform: traces = [7,0,2,0,175,0,-86] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces) # q-expansion: f.q_expansion() # note that sage often uses an isomorphic number field