Magma V2.8 includes packages developed by William Stein and David Kohel as part of a major new initiative in modular forms and modular curves computation. The central object in each package is a finite-rank module equipped with the action of a ring of Hecke operators. The space of modular forms is perhaps the most familiar example of such a Hecke module. Other examples include the space of modular symbols and the group of divisors generated by the supersingular points on the reduction of certain modular curves. This latter module can be computed in some cases using the method of Mestre and Oesterlé [14] and in general using quaternion ideal theory [8,17], which has deep connections with the theory of Shimura curves [11].