The paper is the author’s Ph. D. Thesis, University of Pennsylvania 1989. We quote from his thesis abstract: “The problem we deal with is one of developing a systematic approach – via modular forms - for obtaining refined congruence information on the class number of CM fields. The congruences considered are sharper than those directly implied by the existenc of \(p\)-adic \(L\)-functions and follow from the cuspidal behavior of both the Eisenstein and theta series discussed by P. Deligne and K. A. Ribet in [Invent. Math. 59, 227-286 (1980; Zbl 0434.12009)], as well as the dihedral cusp forms mentioned by J. P. Serre in [Algebraic Number Fields, Proc. Symp. Durham 1975, 193-268 (1977; Zbl 0366.10022)].
Moreover, our approach is designed to prove in a uniform and conceptual manner various class number congruences from the literature, as well as several new ones”.