Counting irreducible sl2 summands using weights zero and one ($\#\text{summands}=\dim V_0+\dim V_1$)

For a finite-dimensional complex sl2 Lie algebra module $V$, the number of simple summands, counted with multiplicity, is $\dim V_0+\dim V_1$. Indeed, the simple module of highest weight $m\ge 0$ has weights $m,m-2,\dots ,-m$, each once. Exactly one of zero and one appears: zero when $m$ is even, one when $m$ is odd. The classification of finite-dimensional sl2 representations decomposes $V$ into these modules, and dimensions of weight spaces add over the direct sum.