  We propose a global Jacquet-Langlands correspondence for the modules over the
von Neumann algebras of $S$-arithmetic subgroups of $\rm{GL}(2)$ and of a
quaternion algebra $D$, which are both defined over a totally real number field
$F$. If a representation $\pi'=\otimes\pi'_v$ of $D^{\times}(\mathbb{A}_F)$
corresponds to a representation $\pi=\otimes \pi_v$ of
$\rm{GL}(2,\mathbb{A}_F)$, we have
$\frac{\dim_{\mathcal{L}(\rm{SL}(2,\mathcal{O}_S))}\pi_S}{\dim_{\mathbb{C}}\pi'_S}=|\frac{\zeta_{D}(0)}{\zeta_{F}(0)}|$,
where $\zeta_F,\zeta_{D}$ are the zeta functions of $F,D$ respectively.
