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We describe the complex multiplication (CM) values of modular functions for$\Gamma_0(N)$ whose divisor is given by a linear combination of Heegnerdivisors in terms of special cycles on the stack of CM elliptic curves. Inparticular, our results apply to Borcherds products of weight $0$ for$\Gamma_0(N)$. By working out explicit formulas for the special cycles, weobtain the prime ideal factorizations of such CM values.

Singular moduli of higher level and special cycles