MSG 201.19

\[\begin{align*} &E_{2}^{1,-1}=\mathbb{Z}^3\\ &E_{1}^{0,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_5}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{D}_5}]\\ &E_{1}^{1,-1}=\mathbb{Z}[\boldsymbol{b}^{(1)}_{b_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{c_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{d_1}]\\ &E_{1}^{2,-1}=0 \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{ccc} b_2 & c_1 & d_1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{cc} \text{A}_5 & \text{D}_5 \\ 1 & 0 \\ 0 & 1 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{cc} 0 & 0 \\ 0 & 0 \\ 0 & 0 \\ \end{array} \right) \end{align*} \]