Some applications of eta-quotients

Abstract

We show that every modular form on Gamma(0)(2(n)) (n >= 2) can be expressed as a sum of eta-quotients, which is a partial answer to Ono's problem. Furthermore, we construct a primitive generator of the ring class field of the order of conductor 4N (N >= 1) in an imaginary quadratic field in terms of the special value of a certain eta-quotient.