${\mathsf{\text{𝖦𝖦𝖲𝖶}}}_{S,\sigma }^{\beta ,l}(M)=\left\{{\{{\mathsf{\text{𝖦𝖫𝖾𝗏}}}_{S,\sigma }^{\beta ,l}(-S_i\cdot M)\}}_{i=0}^{k-1},{\mathsf{\text{𝖦𝖫𝖾𝗏}}}_{S,\sigma }^{\beta ,l}(M)\right\}\in R_{⟨n,q⟩}^{(k+1)\cdot l\cdot (k+1)}$