Weyl dimension formula for B2 ($\dim V(a{\omega }_1+b{\omega }_2)$)

When ${\alpha }_1$ is the short simple root, ${\omega }_1$ is the spin fundamental weight and ${\omega }_2$ is the vector fundamental weight. The Weyl dimension formula gives

For the five-dimensional defining representation $V=V({\omega }_2)$ of ${\mathfrak{so}}_5$, the invariant quadratic form splitsThus the traceless symmetric square is irreducible of dimension $15-1=14$.