A Basis for the space of weakly holomorphic Drinfeld modular forms of level $T$

Abstract

In this article, we explicitly construct a canonical basis for the space of certain weakly holomorphic Drinfeld modular forms for ${\Gamma }_0(T)$ (resp., for ${\Gamma }_0^{+}(T)$) and compute the generating function satisfied by the basis elements. We also give an explicit expression for the action of the $\Theta$-operator, which depends on the divisor of meromorphic Drinfeld modular forms.