Congruences involving the $U_{\ell }$ operator for weakly holomorphic modular forms

Dohoon Choi, Subong Lim

Let $\lambda$ be an integer, and $f(z)={\sum }_{n\gg -\infty }a(n)q^n$ be a weakly holomorphic modular form of weight $\lambda +\frac{1}{2}$ on ${\Gamma }_0(4)$ with integral coefficients. Let $\ell \ge 5$ be…