https://groupprops.subwiki.org/wiki/Standard_representation_of_symmetric_group:S3 Gives two 2-D irreducible representations for S3. One in the basis (e1-e2) and (e2-e3) and another "viewed as a quotient" in the basis $\overline{e1}$ and $\overline{e2}$. There is enough information given about the basis (e1-e2) and (e2-e3) that I can develop the 2-D matrices for it, but there is no information about the basis $\overline{e1}$ and $\overline{e2}$. I am not sure what "viewed as a quotient" would mean in this context.
Could someone please provide an explicit example or cite one illustrating how the $\overline{e1}$ and $\overline{e2}$ basis is used?