Let \(\mathscr{R}_{\alpha}^{\Lambda}\) be the cyclotomic Khovanov-Lauda-Rouquier (KLR) algebra associated with a symmetrizable Kac-Moody Lie algebra \(\frak{g}\) , polynomials {Qij(u, v)}i,j∈I and α in the positive root lattice. Shan et al. (2017) have shown that, when the ground field K has characteristic 0, the degree d component of the cocenter \(\text{Tr}(\mathscr{R}_{\alpha}^{\Lambda})\) is nonzero only if 0 ⩽ d ⩽ dΛα, and the dimension of the degree 0 component \(\text{Tr}(\mathscr{R}_{\alpha}^{\Lambda})_{0}\) is always equal to dim V(Λ)Λ−α, where V(Λ) is the integrable highest weight \(U({\frak{g}})\) -module with the highest weight Λ. In this paper, we show that these results hold for an arbitrary ground field K, arbitrary \(\frak{g}\) and arbitrary polynomials {Qij(u,v)}i,j∈I. We prove these results by generalizing our earlier results (Theorem 1.3 of Hu and Shi (2023)) on the K-linear generators of \(\text{Tr}(\mathscr{R}_{\alpha}^{\Lambda})\) , \(\text{Tr}(\mathscr{R}_{\alpha}^{\Lambda})_{0}\) and \(\text{Tr}({\mathscr{R}}_{\alpha}^{\Lambda})_{d_{\Lambda, \alpha}}\) to arbitrary ground field K, and we give a basis for \(\text{Tr}({\mathscr{R}}_{\alpha}^{\Lambda})_{0}\) .
