Divisibilities and Congruences Identities on Traces of Singular Moduli

Zagier found that traces of singular moduli are the Fourier coefficients of certain modular forms of weight 3/2. As a result, formulas and congruences of these traces are obtained in various situations. Recently, Ahlgen proved a uniform relationship for traces of singular moduli by using the relationship of modular forms with the action of Hecke operators. On the basis of these results, we get some interesting divisibilities and congruences identities on traces of singular moduli and Hurwitz-Kronecker class number.