= Level-two Virasoro descendant Gram matrix
{title2=$G_2=\begin{pmatrix}4h+c/2&6h\\6h&4h(2h+1)\end{pmatrix}$}
For a normalized <highest-weight vector> with $L_0|h\rangle=h|h\rangle$, $L_{n>0}|h\rangle=0$ and $L_n^\dagger=L_{-n}$, the level-two descendants $L_{-2}|h\rangle,L_{-1}^2|h\rangle$ have the displayed <Gram matrix>. It follows from the <Virasoro algebra>: $\langle L_2L_{-2}\rangle=4h+c/2$, $\langle L_2L_{-1}^2\rangle=6h$ and $\langle L_1^2L_{-1}^2\rangle=4h(2h+1)$. At $h=-1,c=26$ its null direction is $(1,3/2)$, giving the <level-two scalar Virasoro null state>. Nullity of a descendant is a metric statement; satisfying all physical constraints must be checked separately.
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