for every normal variation function $\phi \in C^\infty(\Sigma)$. Suppose the real eigenvalues of $L$ are listed with multiplicity in non-increasing order
Then $\Sigma$ is stable, meaning $Q[\phi] \geq 0$ for every $\phi \in C^\infty(\Sigma)$, if and only if $\lambda_1 \leq 0$. Moreover, the Morse index of $\Sigma$ is the number of positive eigenvalues of $L$, counted with multiplicity, and the nullity of $\Sigma$ is the multiplicity of the eigenvalue $0$.