EFFECTIVE COMPUTATION OF DIMENSION FORMULAS FOR MODULAR FORMS TAKING VALUES IN WEIL REPRESENTATIONS (Automorphic Forms, Automorphic L-Functions and Related Topics)

Abstract

Though explicit dimension formulas for vector valued modular forms are well-known they are not efflciently computable as soon as the dimension of the underlying SL(2, mathbb{Z})-module grows. For the case of Weil representations, we describe the tools for simplifying the critical terms in the corresponding dimension formulas in order to obtain formulas which can be rapidly computed.