MSG 132.451

\[\begin{align*} &E_{2}^{1,-1}=0\\ &E_{1}^{0,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_7}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{C}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{C}_7}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{D}_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{D}_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{F}_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{F}_2}]\\ &E_{1}^{1,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{c_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{f_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{g_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{g_3}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{i_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{i_3}]\\ &E_{1}^{2,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\varepsilon _1}] \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{cccccc} c_1 & f_1 & g_1 & g_3 & i_1 & i_3 \\ 0 & -1 & -1 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & -1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & -1 & 0 \\ \frac{1}{2} & \frac{1}{2} & \frac{1}{2} & -\frac{1}{2} & \frac{1}{2} & -\frac{1}{2} \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{cccccccccccc} \text{A}_1 & \text{A}_7 & \text{C}_1 & \text{C}_7 & \text{D}_1 & \text{D}_2 & \text{F}_1 & \text{F}_2 & c_1 & f_1 & g_3 & i_3 \\ 1 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & -2 & 2 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 2 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & -1 & -1 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{cccccc} 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &[V^{(1)}]^{-1}=\left( \begin{array}{ccccccc} c_1 & f_1 & g_1 & g_3 & i_1 & i_3 & \varepsilon _1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 2 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &\Sigma^{(1)}=\left( \begin{array}{c} 1 \\ \end{array} \right) \end{align*} \]