To any finite quadratic module, that is, a finite abelian group together with a non-degenerate quadratic form, it is possible to associate a representation of Mp2(Z), the metaplectic cover of the modular group. This representation is usually referred to as a Weil representation and our main result is a general explicit formula for its matrix coefficients. This result completes earlier work by Scheithauer in the case when the representation factors through SL2(Z). Furthermore, our formula is… CONTINUE READING