Zagier duality for level p weakly holomorphic modular forms

We prove Zagier duality between the Fourier coefficients of canonical bases for spaces of weakly holomorphic modular forms of prime level p with \(11 \le p \le 37\) with poles only at the cusp at \(\infty \), and special cases of duality for an infinite class of prime levels. We derive generating functions for the bases for genus 1 levels.