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Multiplicative -quotients

Authors:	Yves Martin

Institution:	Department of Mathematics, University of California, Berkeley, California 94720

Abstract:	Let $\eta (z)$ be the Dedekind $\eta$ -function. In this work we exhibit all modular forms of integral weight $f(z) = \eta (t_1z)^{r_1}\eta (t_2z)^{r_2}\dots \eta(t_sz)^{r_s}$ , for positive integers and and arbitrary integers , such that both 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 $2 % \mathrm {Co}_1$ via a generalized McKay-Thompson series.

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