MSG 81.36
\[\begin{align*}
&E_{2}^{1,-1}=\mathbb{Z}_2\\
&E_{1}^{0,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{A}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{A}_4}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{B}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{B}_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{C}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{C}_4}]\\
&E_{1}^{1,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{a_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{b_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{e_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{g_2}]\\
&E_{1}^{2,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\alpha _1}]
\end{align*}\]
\[\begin{align*}
&[X^{(1)}]^{-1}=\left(
\begin{array}{cccc}
a_1 & b_1 & e_2 & g_2 \\
0 & 0 & 1 & 0 \\
1 & 0 & -1 & 0 \\
-1 & 1 & 1 & 0 \\
1 & -1 & -1 & 1 \\
\end{array}
\right)\\
&[V^{(0)}]^{-1}=\left(
\begin{array}{cccccc}
\text{A}_3 & \text{A}_4 & \text{B}_1 & \text{B}_2 & \text{C}_3 & \text{C}_4 \\
1 & 1 & 0 & 0 & 0 & 0 \\
0 & 0 & 1 & 1 & 0 & 0 \\
0 & 0 & 0 & 0 & 1 & 1 \\
0 & 0 & 0 & 1 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 1 \\
\end{array}
\right)\\
&\Lambda^{(0)}=\left(
\begin{array}{cccccc}
1 & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 \\
\end{array}
\right)\\
\end{align*}
\]