MSG 206.39

\[\begin{align*} &E_{2}^{1,-1}=0\\ &E_{1}^{0,-1}=\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{A}_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{A}_3}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{A}_4}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{B}_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{B}_3}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{B}_4}]\\ &E_{1}^{1,-1}=\mathbb{Z}[\boldsymbol{b}^{(1)}_{a_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{a_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{c_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{d_3}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{e_1}]\\ &E_{1}^{2,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\alpha _1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(2)}_{\beta _1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\gamma _1}] \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{ccccc} a_1 & a_2 & c_3 & d_3 & e_1 \\ 0 & \frac{1}{2} & -\frac{1}{2} & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ \frac{1}{2} & 0 & 0 & -\frac{1}{2} & 0 \\ 0 & 0 & 0 & 1 & 0 \\ -1 & 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{cccccccc} \text{A}_1 & \text{A}_3 & \text{A}_4 & \text{B}_1 & \text{B}_3 & \text{B}_4 & c_3 & d_3 \\ 1 & 0 & -1 & 0 & 0 & 0 & -1 & 0 \\ 0 & 1 & 1 & 0 & 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 1 & 0 & -1 & 0 & -1 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 & 2 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &[V^{(1)}]^{-1}=\left( \begin{array}{ccccccc} a_1 & a_2 & c_3 & d_3 & e_1 & \alpha _1 & \gamma _1 \\ 1 & 1 & 1 & 0 & -1 & 2 & -2 \\ 0 & 0 & 0 & 1 & 1 & 0 & 2 \\ 0 & -1 & -1 & 1 & 1 & -2 & 4 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &\Sigma^{(1)}=\left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 2 \\ \end{array} \right) \end{align*} \]