MSG 12.63

\[\begin{align*} &E_{2}^{1,-1}=0\\ &E_{1}^{0,-1}=\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{F}_1}]\\ &E_{1}^{1,-1}=\mathbb{Z}[\boldsymbol{b}^{(1)}_{a_1}]\oplus2\mathbb{Z}[\boldsymbol{b}^{(1)}_{c_1}]\oplus2\mathbb{Z}[\boldsymbol{b}^{(1)}_{f_1}]\\ &E_{1}^{2,-1}=2\mathbb{Z}[\boldsymbol{b}^{(2)}_{\alpha _1}]\oplus2\mathbb{Z}[\boldsymbol{b}^{(2)}_{\beta _1}]\oplus2\mathbb{Z}[\boldsymbol{b}^{(2)}_{\gamma _1}] \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{ccc} a_1 & c_1 & f_1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{c} \text{F}_1 \\ 1 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{c} 1 \\ \end{array} \right)\\ &[V^{(1)}]^{-1}=\left( \begin{array}{ccc} a_1 & c_1 & f_1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{array} \right)\\ &\Sigma^{(1)}=\left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 0 \\ \end{array} \right) \end{align*} \]