On the cusp form motives in genus 1 and level 1

Abstract

We prove that the moduli space of stable $n$-pointed curves of genus 1 and the projector associated to the alternating representation of the symmetric group on $n$ letters define (for $n \gt 1$) the Chow motive corresponding to cusp forms of weight $n + 1$ for $\mathrm{SL}(2, \mathbb{Z})$. This provides an alternative (in level 1) to the construction of Scholl.