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We extend a result of Ahlgren and Ono (Compos. Math. 141, 293–312, 2005) on congruences for traces of singular moduli of level 1 to traces defined in terms of Hauptmodul associated to certain groups of genus 0 of higher levels.
Let p be a prime and f(z)=∑na(n)qn be a weakly holomorphic modular function for $\varGamma _{0}^{*}(p^{2})$ with a(0)=0. We use Bruinier and Funke’s work to find the generating series of modular traces of f(z) as Jacobi forms. And as an application we construct Borcherds products related to the Hauptmoduln for genus zero groups $\varGamma _{0}^{*}(p^{2})$ .
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