# SageMath code for working with modular form 405.3.l.g # Compute space of new eigenforms: from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 9])) N = Newforms(chi, 3, 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