Vanishing of weight-fourteen level-one cusp forms ($S_{14}(S{L}_2(\mathbb{Z}))=0$)

A nonzero weight-fourteen cusp form would have order at infinity at least one and order at $i$ at least one, since $i^{14}=-1$. The valence formula for the modular group would then give $1+1/2\le 14/12$, which is impossible.