  We study the rational Cherednik algebra $H_{t,c}(S_3,\h)$ of type $A_2$ in
positive characteristic $p$, and its irreducible category $\mathcal{O}$
representations $L_{t,c}(\tau)$. For every possible value of $p,t,c$, and
$\tau$ we calculate the Hilbert polynomial and the character of
$L_{t,c}(\tau)$, and give explicit generators of the maximal proper graded
submodule of the Verma module.
