I am working on the chamber homology for $SL(2,F)$, and stuck at some basic stuff on D.S. reps of $SL(2,F)$.

If $J_{0}=SL(2,\mathcal{O})\cap SL(2,F)$ and $J_{1}=(wJ_{0}w^{-1})\cap SL(2,F)$ are two max. subgroups of $SL(2,F)$ where $ w= \left( \begin{array}{cc} 0 & 1 \\ \varpi_{\mathbb{F}} & 0 \\ \end{array} \right)$, $\varpi$ is the uniformizer and let $I=J_{0}\cap J_{1}$ be Iwahori subgroup.

Just wondering if anybody knows how can I induce a cuspidal reps(D.S.) from a charachter belong to $J_{0}$ or/and $J_{1}$?