  In this paper we find the number of homogeneous polynomials of degree d such
that they vanish on cuspidal modular forms of even weight $m\geq 2$ that form a
basis for $S_m(\Gamma_0(N))$. We use these cuspidal forms to embedd $X_0(N)$ to
projective space and we find the Hilbert polynomial of the graded ideal of the
projective curve that is the image of this embedding.
