Let $R,S$ be arbitrary associative rings and ${}_R{C}_S$ a semidualizing bimodule. We give some equivalent characterizations for $R$ being left coherent (and right perfect) rings, left Noetherian rings and left Artinian rings in terms of the $C$-( $\text{FP}$-)injectivity, flatness and projectivity of character modules of certain left $S$-modules.