MSG 83.45

\[\begin{align*} &E_{2}^{1,-1}=\mathbb{Z}^2\\ &E_{1}^{0,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{C}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{D}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{F}_3}]\\ &E_{1}^{1,-1}=2\mathbb{Z}[\boldsymbol{b}^{(1)}_{e_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{e_2}]\oplus2\mathbb{Z}[\boldsymbol{b}^{(1)}_{g_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{g_2}]\\ &E_{1}^{2,-1}=0 \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{cccc} e_1 & e_2 & g_1 & g_2 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{cccccc} \text{A}_3 & \text{C}_3 & \text{D}_3 & \text{F}_3 & e_2 & g_2 \\ 1 & 0 & 1 & 0 & 2 & 0 \\ 0 & 1 & 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{cccccc} 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right) \end{align*} \]