2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224845$N=2$ coset models of the type $SU(m+1)/SU(m)\times U(1)$ with nondiagonal modular invariants for both $SU(m+1)$ and $SU(m)$ are considered. Poincaré polynomials of the corresponding chiral rings of these algebras are constructed. They are used to compute the number of chiral generations of the associated string compactifications. Moddings by discrete symmetries are also discussed.22 pages, (RevTex), preprint GTCRG-92-1 and CNEA-CAB-039/92. % Minor changes in the resultsHigh Energy Physics - Theorytext