# SageMath code for working with modular form 9025.2.a.h # Compute space of new eigenforms: from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9025, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a") # select newform: traces = [1,1,0,-1,0,0,2,-3,-3,0,-4,0,2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces) # q-expansion: f.q_expansion() # note that sage often uses an isomorphic number field