  To a finite quadratic module, that is, a finite abelian group D together with
a non-singular quadratic form Q:D --> Q/Z, it is possible to associate a
representation of either the modular group, SL(2,Z), or its metaplectic cover,
Mp(2,Z), on C[D], the group algebra of D. This representation is usually called
the Weil representation associated to the finite quadratic module. The main
result of this paper is a general explicit formula for the matrix coefficients
of this representation. The formula, which involves the p-adic invariants of
the quadratic module, is given in a way which is easy to implement on a
computer. The result presented completes an earlier result by Scheithauer for
the Weil representation associated to a discriminant form of even signature.
