MSG 220.90

\[\begin{align*} &E_{2}^{1,-1}=\mathbb{Z}_2\\ &E_{1}^{0,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{A}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{A}_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{A}_3}]\\ &E_{1}^{1,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{a_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{c_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{c_2}]\\ &E_{1}^{2,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\alpha _1}] \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{ccc} a_1 & c_1 & c_2 \\ 0 & 1 & 1 \\ 1 & 0 & 0 \\ -1 & 0 & 1 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 0 & 0 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{ccc} \text{A}_1 & \text{A}_2 & \text{A}_3 \\ 1 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{array} \right)\\ &[V^{(1)}]^{-1}=\left( \begin{array}{ccc} a_1 & c_1 & c_2 \\ 0 & 1 & 1 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ \end{array} \right)\\ &\Sigma^{(1)}=\left( \begin{array}{ccc} 1 & 0 & 0 \\ \end{array} \right) \end{align*} \]