Let $k \ge 2$, let $N \ge 1$, let $p$ be a prime with $p \nmid N$, and let $f(q)=\sum_{m\ge 0} a_m q^m$ be a complex modular form in $M_k(\Gamma_0(N);\mathbb{C})$. The action induced by the normalized geometric correspondence $T_p$ on modular forms is the classical operator