Structure of the module of vector-valued modular forms
نویسندگان
چکیده
Let V be a representation of the modular group Γ 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 Γ-modules to graded M-lattices and give some applications, including the calculation of the Hilbert-Poincaré of H(V ) in some cases. MSC 11F99, 13C05
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