Consider as a -module of itself.

Then, M is decomposed as (Dummit & Foote p869-870)

, where .

Each is a submodule of M (two-sided ideal of M) and your correspond to , respectively.

Since has three conjugacy classes, there are three irreducible characters of .

The is the ideal you are looking for, where .

Note that has a dimension 4, which is not irreducible.