Two-index symmetric representation (${\mathrm{Sym}}^{2}V$)

The two-index symmetric representation of $SU(N)$ is the symmetric square of its fundamental representation. For $N\ge 3$, it has dimension $N(N+1)/2$, Dynkin index $N+2$, and cubic anomaly coefficient $N+4$ when the fundamental index and anomaly are normalized to one. For $N=2$, the Dynkin index formula still applies in the stated normalization, but every symmetric cubic trace vanishes, so the stated fundamental-normalized cubic anomaly coefficient is not defined.