MSG 88.82

\[\begin{align*} &E_{2}^{1,-1}=\mathbb{Z}_2\\ &E_{1}^{0,-1}=\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{C}_1}]\\ &E_{1}^{1,-1}=\mathbb{Z}[\boldsymbol{b}^{(1)}_{d_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{e_1}]\\ &E_{1}^{2,-1}=\mathbb{Z}[\boldsymbol{b}^{(2)}_{\delta _1}] \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{cc} d_1 & e_1 \\ 1 & 0 \\ 0 & 1 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{c} \text{C}_1 \\ 1 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{c} -2 \\ \end{array} \right)\\ &[V^{(1)}]^{-1}=\left( \begin{array}{cc} d_1 & e_1 \\ 1 & 0 \\ 0 & 1 \\ \end{array} \right)\\ &\Sigma^{(1)}=\left( \begin{array}{cc} 2 & 0 \\ \end{array} \right) \end{align*} \]