On the restriction of some irreducible mod-p representations of GL₂(Fq) to GL₂(Fₚ)

For a prime $p,$ let Fq be a finite extension of Fₚ and G=GL₂(Fq). Then the irreducible representations of G are classified as twists of Symr⃗( F̄p²). The restriction of irreducibles of G to its subgroup G=GL₂(Fₚ) is same as investigating the behavior of the tensor product of irreducible representations of $G.$ In this paper, we study the restriction of some of these representations of G to $G,$ for $2$ and $3$ degree extensions of Fₚ.