# SageMath code for working with modular form 20070.2.a.bh # Compute space of new eigenforms: from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(20070, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))] # Compute space of new eigenforms: from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(20070, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a") # select newform: traces = [1,1,0,1,1,0,1,1,0,1,0,0,2,1,0,1,3,0,-5,1,0,0,0,0,1,2,0,1,-5, 0,0,1,0,3,1,0,-5,-5,0,1,-10,0,-8,0,0,0,-10,0,-6,1,0,2,4,0,0,1,0,-5,-13, 0,-11,0,0,1,2,0,3,3,0,1,8,0,8,-5,0,-5,0,0,-13,1,0,-10,-11,0,3,-8,0,0,-10, 0,2,0,0,-10,-5,0,7,-6,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces) # q-expansion: f.q_expansion() # note that sage often uses an isomorphic number field