  We consider a natural extension of the Petersson scalar product to the entire
space of modular forms of integral weight $k\ge 2$ for a finite index subgroup
of the modular group. We show that Hecke operators have the same adjoints with
respect to this inner product as for cusp forms, and we show that the Petersson
product is nondegenerate for $\Gamma_1(N)$ and $k>2$. For $k=2$ we give
examples when it is degenerate, and when it is nondegenerate.
