 Low-dimensional SU3 tensor representations

The six smallest complex irreducible representations of SU(3) have highest weights $(0,0),(1,0),(0,1),(2,0),(0,2),(1,1)$ and dimensions $1,3,3,6,6,8$. Their Young diagram row lengths are $(0,0),(1,0),(1,1),(2,0),(2,2),(2,1)$. They are realized by scalars, defining vectors, covectors (equivalently antisymmetric tensors of degree two), upper and lower symmetric tensors of degree two, and mixed tensors $T^i{}_j$ with zero trace, respectively. The Weyl dimension formula is $\dim (p,q)=(p+1)(q+1)(p+q+2)/2$. For $p+q\ge 3$ this is at least ten, proving that the list exhausts the six smallest representations.