  In this paper, we give a new genus-4 topological recursion relation for
Gromov-Witten invariants of compact symplectic manifolds via Pixton's relations
on the moduli space of curves. As an application, we prove Pixton's relations
imply a known topological recursion relation on $\bar{\mathcal{M}}_{g,1}$ for
genus $g\leq4$.
