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Recently, a weak converse theorem for Borcherds' lifting operator of type$O(2,1)$ for $\G_0(N)$ is proved and the logarithmic derivative of a modularform for $\G_0(N)$ is explicitly described in terms of the values ofNiebur-Poincar\'e series at its divisors in the complex upper half-plane. Inthis paper, we prove that the generalized Borcherds' lifting operator of type$O(2,1)$ is Hecke equivariant under the extension of Guerzhoy's multiplicativeHecke operator on the integral weight meromorphic modular forms and the Heckeoperator on half-integral weight vector-valued harmonic weak Maass forms.Additionally, we show that the logarithmic differential operator is also Heckeequivariant under the multiplicative Hecke operator and the Hecke operator onintegral weight meromorphic modular forms. As applications of Heckeequivariance of the two operators, we obtain relations for twisted traces ofsingular moduli modulo prime powers and congruences for twisted class numbersmodulo primes, including those associated to genus $1$ modular curves.

Hecke equivariance of generalized Borcherds products of type $O(2,1)$