  We develop a simple algebraic approach to the study of the Weil
representation associated to a finite abelian group. As a result, we obtain a
simple proof of a generalisation of a well-known formula for the absolute value
of its character. We also obtain a new result about its decomposition into
irreducible representations. As an example, the decomposition of the Weil
representation of Sp_{2g}(Z/NZ) is described for odd N.
