MSG 47.256

\[\begin{align*} &E_{2}^{1,-1}=\mathbb{Z}_2\\ &E_{1}^{0,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_5}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_6}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{B}_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{B}_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{B}_5}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{B}_6}]\\ &E_{1}^{1,-1}=\mathbb{Z}[\boldsymbol{b}^{(1)}_{a_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{a_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{a_3}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{a_4}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{b_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{b_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{c_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{c_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{i_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{i_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{j_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{j_2}]\\ &E_{1}^{2,-1}=\mathbb{Z}[\boldsymbol{b}^{(2)}_{\alpha _1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(2)}_{\alpha _2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\gamma _1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(2)}_{\delta _1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(2)}_{\varepsilon _1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(2)}_{\varepsilon _2}] \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{cccccccccccc} a_1 & a_2 & a_3 & a_4 & b_1 & b_2 & c_1 & c_2 & i_1 & i_2 & j_1 & j_2 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & -1 \\ 0 & 0 & 0 & 0 & \frac{1}{2} & \frac{1}{2} & 0 & 0 & -\frac{1}{2} & -\frac{1}{2} & 0 & 0 \\ 0 & 0 & 2 & -1 & 1 & 1 & -2 & 0 & -1 & -1 & 0 & 2 \\ 0 & 1 & 1 & 0 & 0 & 0 & 0 & 2 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 1 & 0 & 0 & 2 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & -1 & -1 & 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & -1 & 0 & 0 & -2 & 0 & 0 & 0 & 0 & 2 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{cccccccccccc} \text{A}_1 & \text{A}_2 & \text{A}_5 & \text{A}_6 & \text{B}_1 & \text{B}_2 & \text{B}_5 & \text{B}_6 & b_1 & b_2 & i_1 & i_2 \\ 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 2 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 \\ 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & -2 & 2 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & -1 & -1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 & 1 & -1 & -1 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{cccccccc} 1 & 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 & 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 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 \\ \end{array} \right)\\ &[V^{(1)}]^{-1}=\left( \begin{array}{ccccccccccccc} a_1 & a_2 & a_3 & a_4 & b_1 & b_2 & c_1 & c_2 & i_1 & i_2 & j_1 & j_2 & \gamma _1 \\ 1 & 0 & 0 & 1 & 0 & 0 & 0 & -2 & 0 & 0 & 2 & 2 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 0 & 0 \\ 0 & 0 & 1 & -1 & 0 & 0 & 0 & 2 & 0 & 0 & -2 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & -1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &\Sigma^{(1)}=\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 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right) \end{align*} \]