Let F=GF(p^k) be any finite field. Let G be a group of all affine permutations on F (i.e. permutations of form ax+b). Then the set of all functions from F to \bar{F} is a linear representation of G, where g(f)=f(gx).

What are all sub-representations of this representation? Is it possible to characterize them?

Note: that in this case gcd(|G|,F) not equal to 1.