# SageMath code for working with modular form 1200.3.bg.b # Compute space of new eigenforms: from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1200, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 3])) N = Newforms(chi, 3, names="a") # select newform: traces = [4,0,0,0,0,0,-16,0,0,0,8,0,0,0,0,0,16,0,0,0,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(21)] == traces) # q-expansion: f.q_expansion() # note that sage often uses an isomorphic number field