A special case of Haiman's identity for the character of the quotient ring of diagonal coinvariants under the diagonal action of the symmetric group yields a formula for the bigraded Hilbert series as a sum of rational functions in $q,t$. In this talk I will show how a summation identity of Garsia and Zabrocki for Macdonald polynomial Pieri coefficients can be used to transform Haiman's formula for the Hilbert series into an explicit polynomial in $q,t$ with integer coefficients. An equivalent formulation expresses the Hilbert series as the constant term in a certain multivariate Laurent series.