On the zeros of certain weakly holomorphic modular forms for ${\varGamma }_0^+(5)$ and ${\varGamma }_0^+(7)$

Abstract

Let $p$ be a prime for which $\Gamma _0^+(p)$ is of genus zero, and let $M_k^!(\Gamma _0^+(p))$ be the space of weakly holomorphic modular forms of weight $k$ for $\Gamma _0^+(p) $. It is known that $M_k^!(\Gamma _0^+(p))$ has the natural basis. In this p