  Let $F$ be a finite extension of $\mathbb{Q}_p$, let $\Omega_F$ be Drinfeld's
upper half-plane over $F$ and let $G^0$ the subgroup of $GL_2(F)$ consisting of
elements whose determinant has norm $1$. Let $\mathscr{L}$ be a torsion
$G^0$-equivariant line bundle with connection on $\Omega_F$. We show that the
strong dual of $\mathscr{L}(\Omega_F)$ is an admissible locally $F$-analytic
representation of $G^0$ of topological length at most $2$. It is topologically
irreducible if and only if the underlying connection on $\mathscr{L}$ is
non-trivial. We give an explicit formula for the length of the strong dual of
the space of globally-defined rigid analytic functions on a $G^0$-equivariant
finite \'etale rigid analytic covering of $\Omega_F$ with abelian Galois group
as an admissible locally $F$-analytic representation of $G^0$.
