Polynomials on cusp forms for Γ0(N) and triangle of numbers

In this presentation we compute the bases of homogeneous polynomials of degree d such that they vanish on cuspidal modular forms of even weight m2 that form a basis for Sm(Γ0(N)). Among them we find the polynomials that are irreducible. We observe the calculated numbers of such polynomials and arrange them in triangle of numbers for which we present some interesting properties regarding to Pascal and Rascal triangle