Can a Drinfeld module be modular?

Let $k$ be a global function field with field of constants $\text{Fr}$ and let $\mathrm{\infty }$ be a fixed place of $k$. In his habilitation thesis \cite{boc2}, Gebhard B"ockle attaches abelian Galois representations to characteristic $p$ valued cusp eigenforms and double cusp eigenforms \cite{go1} such that Hecke eigenvalues correspond to the image of Frobenius elements. In the case where $k=\text{Fr}(T)$ and $\mathrm{\infty }$ corresponds to the pole of $T$, it then becomes reasonable to ask whether rank 1 Drinfeld modules over $k$ are themselves ``modular’’ in that their Galois representations arise from a cusp or double cusp form. This paper gives an introduction to \cite{boc2} with an emphasis on modularity and closes with some specific questions raised by B"ockle’s work.