Assume that there exist a norm $\lVert\mathord{\cdot}\rVert_{1}$ on $V_{1}(L)$ such that $\phi$ is equal to $\mathrm{FS}(\lVert\mathord{\cdot}\rVert_{1})$. Then for any $n\in\mathbb{N}$, $\mathrm{FS}(\lVert\mathord{\cdot}\rVert_{n\phi})$ is equal to $n\phi$. ([CMor18, Proposition 3.3])