MSG 161.70

\[\begin{align*} &E_{2}^{1,-1}=\mathbb{Z} \times \mathbb{Z}_2\\ &E_{1}^{0,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_3}]\\ &E_{1}^{1,-1}=\mathbb{Z}[\boldsymbol{b}^{(1)}_{a_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{e_1}]\\ &E_{1}^{2,-1}=\mathbb{Z}[\boldsymbol{b}^{(2)}_{\beta _1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(2)}_{\delta _1}] \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{cc} a_3 & e_1 \\ 0 & 1 \\ 1 & 0 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{cc} \text{A}_3 & e_1 \\ 0 & 1 \\ -1 & 1 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{cc} 2 & 0 \\ 0 & 0 \\ \end{array} \right)\\ &[V^{(1)}]^{-1}=\left( \begin{array}{cc} a_3 & e_1 \\ 1 & 0 \\ 0 & 1 \\ \end{array} \right)\\ &\Sigma^{(1)}=\left( \begin{array}{cc} 0 & 0 \\ 0 & 0 \\ \end{array} \right) \end{align*} \]