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In a chromomagnetic model, we analyse the properties of the newly observed$P_c(4457)^+$, $P_c(4440)^+$, and $P_c(4312)^+$ states. We estimate the massesof the $(uud)_{8_c}(c\bar{c})_{8_c}$ and $(uds)_{8_c}(c\bar{c})_{8_c}$pentaquark states by considering the isospin breaking effects. Their values aredetermined by calculating mass distances from the $\Sigma_c^{++}D^-$ and$\Xi_c^{\prime+}D^-$ thresholds, respectively. It is found that the isospinbreaking effects on the spectrum are small. From the uncertainty considerationand the rearrangement decay properties in a simple model, we find that it ispossible to assign the $P_c(4457)^+$, $P_c(4440)^+$, and $P_c(4312)^+$ as$J^P=3/2^-$, $1/2^-$, and $3/2^-$ pentaquark states, respectively. Theassignment in the molecule picture can be different, in particular for the$P_c(4312)^+$. The information from open-charm channels, e.g. ${\calB}[P_c\to\Sigma_c^{++}D^-]/{\cal B}[P_c\to J/\psi p]$, will play an importantrole in distinguishing the inner structures of the $P_c$ states. Discussionsand predictions based on the calculations are also given.

$P_c(4457)^+$, $P_c(4440)^+$, and $P_c(4312)^+$: molecules or compact pentaquarks?