Coinvariants and the regular representation of a cyclic P-group

We consider an indecomposable representation of a cyclic p-group ${Z_{p^r}}$ over a field of characteristic p. We show that the top degree of the corresponding ring of coinvariants is less than ${frac{(r^2+3r)p^r}{2}}$ . This bound also applies to the degrees of the generators for the invariant ring of the regular representation.