MSG 162.75

\[\begin{align*} &E_{2}^{1,-1}=\mathbb{Z}_2^3\\ &E_{1}^{0,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{A}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{B}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{C}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{D}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{E}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{F}_3}]\\ &E_{1}^{1,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{a_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{b_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{c_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{d_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{e_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{f_3}]\\ &E_{1}^{2,-1}=0 \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{cccccc} a_3 & b_3 & c_3 & d_3 & e_3 & f_3 \\ 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & -1 & 1 & 0 & 0 \\ -1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & -1 & 1 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{cccccc} \text{A}_3 & \text{B}_3 & \text{C}_3 & \text{D}_3 & \text{E}_3 & \text{F}_3 \\ 1 & 0 & 0 & 1 & 0 & 0 \\ 0 & 1 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{cccccc} 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\\ \end{align*} \]