MSG 82.40

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

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{cc} d_1 & e_1 \\ 1 & 0 \\ 0 & 1 \\ \end{array} \right)\\ \end{align*} \]