# SageMath code for working with modular form 416.2.bd.a # Compute space of new eigenforms: from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 7, 6])) N = Newforms(chi, 2, names="a") # select newform: f = N[0] # Warning: the index may be different # q-expansion: f.q_expansion() # note that sage often uses an isomorphic number field