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Let Γ be a genus 0 group between Γ 0 (N ) and its normalizer in SL 2 (R) where N is squarefree. We construct an automorphic product on Γ × Γ and determine its sum expansions at the different cusps. We obtain many new product identities generalizing the classical product formula of the elliptic j-function due to Zagier, Borcherds and others. These results imply that the moonshine conjecture for Conway's group Co 0 is true for elements of squarefree level.doi:10.1515/crelle.2008.092 fatcat:5svzrpdowzadzmguevruavxbvy