MSG 164.90

\[\begin{align*} &E_{2}^{1,-1}=0\\ &E_{1}^{0,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{A}_5}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{A}_6}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{C}_3}]\\ &E_{1}^{1,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{a_3}]\\ &E_{1}^{2,-1}=0 \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{c} a_3 \\ 1 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{ccc} \text{A}_5 & \text{A}_6 & \text{C}_3 \\ 1 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{ccc} 1 & 0 & 0 \\ \end{array} \right)\\ \end{align*} \]