Resumen de Structure of the module of vector-valued modular forms

Christopher Marks, Geoffrey Mason

• Let V be a representation of the modular group �¡ of dimension p. We show that the Z-graded space H(V ) of holomorphic vector-valued modular forms associated to V is a free module of rank p over the algebra M of classical holomorphic modular forms. We study the nature of H considered as a functor from �¡-modules to graded M-lattices and give some applications, including the calculation of the Hilbert.Poincar�Le series of H(V ) in some cases.