  A holomorphic discrete series representation $(L_\pi,H_\pi)$ of a connected
semi-simple real Lie group $G$ is associated with an irreducible representation
$(\pi,V_{\pi})$ of its maximal compact subgroup $K$. The underlying space
$H_\pi$ can be realized as certain holomorphic $V_{\pi}$-valued functions on
the bounded symmetric domain $\mathcal{D}\cong G/K$. By the Berezin
quantization, we transfer $B(H_{\pi})$ into End$(V_{\pi})$-valued functions on
$\mathcal{D}$. For a lattice $\Gamma$ of $G$, we give the formula of a faithful
normal tracial state on the commutant $L_\pi(\Gamma)'$ of the group von Neumann
algebra $L_{\pi}(\Gamma)''$. We find the Toeplitz operators $T_f$'s associated
with essentially bounded End$(V_\pi)$-valued functions $f$'s on
$\Gamma\backslash\mathcal{D}$ generate the entire commutant $L_\pi(\Gamma)'$:
$$\overline{\{T_f|f\in L^\infty(\Gamma\backslash\mathcal{D},{\rm
End}(V_\pi))\}}^{\text{w.o.}}=L_\pi(\Gamma)'.$$ For any cuspidal automorphic
form $f$ defined on $G$ (or $\mathcal{D}$) for $\Gamma$, we find the associated
Toeplitz-type operator $T_f$ intertwines the actions of $\Gamma$ on these
square-integrable representations. Hence the composite operator of the form
$T_g^{*}T_f$ belongs to $L_\pi(\Gamma)'$. We prove these operators span
$L^{\infty}(\Gamma\backslash\mathcal{D})$ and
$$\overline{\langle\{\text{span}_{f,g} T_g^{*}T_f\}\otimes {\rm
End}(V_\pi)\rangle}^{\text{w.o.}}=L_\pi(\Gamma)',$$ where $f,g$ run through
holomorphic cusp forms for $\Gamma$ of same types. If $\Gamma$ is an infinite
conjugacy classes group, we obtain a $\text{II}_1$ factor from cusp forms.
