quantum mechanics - How to determine whether an eigenstate of total spin is symmetric or antisymmetric?

Here we have two identical paticles with spin $I$, integer or half-integer, and there are $(2I+1)^2$ states.

Each one of them can be uniquely determined by total spin and its orientation, we can use $|J,m\rangle$ to represent this state. And because of its uniqueness, it is either symmetric or antisymmetric.

How to determine whether $|J,m\rangle$ is symmetric or antisymmetric based on $I$, $J$ and $m$?