MSG 13.67

\[\begin{align*} &E_{2}^{1,-1}=\mathbb{Z}^2\\ &E_{1}^{0,-1}=\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{E}_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{F}_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{G}_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{H}_1}]\\ &E_{1}^{1,-1}=2\mathbb{Z}[\boldsymbol{b}^{(1)}_{b_1}]\oplus2\mathbb{Z}[\boldsymbol{b}^{(1)}_{g_1}]\\ &E_{1}^{2,-1}=0 \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{cc} b_1 & g_1 \\ 1 & 0 \\ 0 & 1 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{cccc} \text{E}_1 & \text{F}_1 & \text{G}_1 & \text{H}_1 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{cccc} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ \end{array} \right) \end{align*} \]