\[\theta\left(\frac{\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}}{2}\middle|%
\boldsymbol{{\Omega}}\right)\theta\left(\frac{\mathbf{x}+\mathbf{y}-\mathbf{u}%
-\mathbf{v}}{2}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\frac{\mathbf{x%
}-\mathbf{y}+\mathbf{u}-\mathbf{v}}{2}\middle|\boldsymbol{{\Omega}}\right)%
\theta\left(\frac{\mathbf{x}-\mathbf{y}-\mathbf{u}+\mathbf{v}}{2}\middle|%
\boldsymbol{{\Omega}}\right)=\frac{1}{2^{g}}\sum_{\boldsymbol{{\alpha}}\in%
\frac{1}{2}{\mathbb{Z}}^{g}/{\mathbb{Z}}^{g}}\,\sum_{\boldsymbol{{\beta}}\in%
\frac{1}{2}{\mathbb{Z}}^{g}/{\mathbb{Z}}^{g}}e^{2\pi i\left(2\boldsymbol{{%
\alpha}}\cdot\boldsymbol{{\Omega}}\cdot\boldsymbol{{\alpha}}+\boldsymbol{{%
\alpha}}\cdot[\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}]\right)}\*\theta%
\left(\mathbf{x}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta%
}}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\mathbf{y}+\boldsymbol{{%
\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}\middle|\boldsymbol{{\Omega}%
}\right)\theta\left(\mathbf{u}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+%
\boldsymbol{{\beta}}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\mathbf{v}%
+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}\middle|%
\boldsymbol{{\Omega}}\right),\]