MSG 86.72

\[\begin{align*} &E_{2}^{1,-1}=\mathbb{Z} \times \mathbb{Z}_2\\ &E_{1}^{0,-1}=\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{A}_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{A}_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{A}_5}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{A}_6}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{C}_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{D}_1}]\\ &E_{1}^{1,-1}=\mathbb{Z}[\boldsymbol{b}^{(1)}_{a_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{b_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{e_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{e_3}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{g_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{g_3}]\\ &E_{1}^{2,-1}=\mathbb{Z}[\boldsymbol{b}^{(2)}_{\alpha _1}] \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{cccccc} a_1 & b_1 & e_1 & e_3 & g_1 & g_3 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 1 & 0 & -1 & 2 & 1 & 0 \\ 1 & 0 & -1 & 1 & 2 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{cccccc} \text{A}_1 & \text{A}_2 & \text{A}_5 & \text{A}_6 & \text{C}_1 & \text{D}_1 \\ 1 & 1 & 0 & 0 & 0 & -1 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & -2 & 1 & 3 & 1 & -1 \\ 0 & -1 & 0 & 1 & 1 & 0 \\ 0 & -1 & 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{cccccc} 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\\ &[V^{(1)}]^{-1}=\left( \begin{array}{cccccc} a_1 & b_1 & e_1 & e_3 & g_1 & g_3 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &\Sigma^{(1)}=\left( \begin{array}{cccccc} 2 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right) \end{align*} \]