modular forms, being some of the most fundamental objects in number theory, have a habit of appearing in many different contexts; such coincidences turn out to be extremely useful for computational purposes. i'll describe three different constructions that give the action of the hecke operators on certain spaces of modular forms: the classical method of modular symbols (manin), the``method of graphs'' based on isogenies among supersingular elliptic curves (mestre-oestrele), and a less well-known method based of reduction of quadratic forms (birch).