Vanishing of weight-fourteen level-one cusp forms
= Vanishing of weight-fourteen level-one cusp forms
{title2=$S_{14}(SL_2(\mathbb Z))=0$}
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 $1+1/2\leq14/12$, which is impossible.