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In this paper we study regularized Petersson products between a holomorphictheta series associated to a positive definite binary quadratic form and aweakly holomorphic weight 1 modular form with integral Fourier coefficients. Inour recent work \cite{Via CM Green} motivated by the conjecture of B. Gross andD. Zagier on the CM values of higher Green's functions we have discovered thatsuch a Petersson product is equal to the logarithm of a certain algebraicnumber lying in a ring class field associated to the binary quadratic form. Themain result of the present paper is the explicit factorization formula for theobtained algebraic number.

Petersson inner products of weight one modular forms