MSG 189.226

\[\begin{align*} &E_{2}^{1,-1}=\mathbb{Z}_2^2\\ &E_{1}^{0,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{A}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{A}_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{A}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{B}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{D}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{E}_1}]\\ &E_{1}^{1,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{b_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{b_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{g_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{g_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{g_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{h_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{h_2}]\\ &E_{1}^{2,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\varepsilon _1}] \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{ccccccc} b_1 & b_2 & g_1 & g_2 & g_3 & h_1 & h_2 \\ 1 & 1 & 1 & 1 & 0 & 1 & 1 \\ 0 & 1 & 0 & 0 & -1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & -1 & 1 & 0 & 1 & 1 & 0 \\ 0 & 0 & -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & -1 & 1 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{cccccc} 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{cccccc} \text{A}_1 & \text{A}_2 & \text{A}_3 & \text{B}_1 & \text{D}_1 & \text{E}_1 \\ 1 & 0 & 0 & 0 & 0 & -1 \\ 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &[V^{(1)}]^{-1}=\left( \begin{array}{ccccccc} b_1 & b_2 & g_1 & g_2 & g_3 & h_1 & h_2 \\ 1 & 1 & 1 & 1 & 0 & 1 & 1 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &\Sigma^{(1)}=\left( \begin{array}{ccccccc} 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right) \end{align*} \]