We find an intriguing relation between the chiral algebra and the mixed Hodge structure of the Coulomb branch of four dimensional $𝒩=2$ superconformal field theories. We identify the space of irreducible characters of the $𝒩=4$ $SU(N)$ chiral algebra $𝕍[{𝒯}_{SU(N)}]$ by analytically computing the Wilson line Schur index, and imposing modular invariance. We further establish a map from the $𝕍[{𝒯}_{SU(N)}]$ characters to the characters of the ${𝒯}_{p,N}$ chiral algebra. We extract the pure part of the mixed Hodge polynomial $P{H}_c$ of the Coulomb branch compactified on a circle, and prove that $P{H}_c$ encodes the representation theory of $𝕍[{𝒯}_{SU(N)}]$. We expect this to be a new entry of the 4D mirror symmetry framework.