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We study the cocenter of the cyclotomic quiver Hecke algebra$R^\Lambda_\alpha$ associated to an {\it arbitrary} symmetrizable Cartan matrix$A=(a_{ij})_{i,j}\in I$, $\Lambda\in P^+$ and $\alpha\in Q_n^+$. We introduce anotion called "piecewise dominant sequence" and use it to construct someexplicit homogeneous elements which span the maximal degree component of thecocenter of $R^\Lambda_\alpha$. We show that the minimal degree components ofthe cocenter of $R^\Lambda_\alpha$ is spanned by the image of some KLRidempotent $e(\nu)$, where each $\nu\in I^\alpha$ is piecewise dominant. As anapplication, we show that the weight space $L(\Lambda)_{\Lambda-\alpha}$ of theirreducible highest weight module $L(\Lambda)$ over $\mathfrak{g}(A)$ isnonzero (equivalently, $R^\Lambda_\alpha\neq 0$) if and only if there exists apiecewise dominant sequence $\nu\in I^\alpha$.

Piecewise dominant sequences and the cocenter of the cyclotomic quiver Hecke algebras