Abstract

Let eta(z) be the Dedekind eta-function. In this work we exhibit all modular forms of integral weight f(z) = eta(t(1)z)(r)1 eta(t(2)z)(r2)...eta(t(s)z)(rs), for positive integers s and t(j) and arbitrary integers r(j), such that both f(z) and its image under the Fricke involution are eigenforms of all Hecke operators. We also relate most of these modular forms with the Conway group 2Co(1) via a generalized McKay-Thompson series.