Bimodular forms with given residues

Let $Y_0(1)$ be a modular curve and $T_N$ be a curve which is the graph of the $N$-th modular Hecke correspondence embedded in $Y_0 (1) х Y_0 (1)$. For a finite subset S of natural numbers consider the divisor $D_S$ which is the union of the modular correspondences. A non compact surface that is the complement to this divisor is denoted by $Y_S$. It is well known that in case of the divisor with normal crossings, the cohomology of the complement of the divisor on a nonsingular complex manifold is expressed in terms of the cohomology of the complex of differential forms with logarithmic poles along the divisor.
I'll talk about the construction of such differential forms with given residues on the non compact surface $Y(1, N)$.