Let $G=GL(2,p)$ be a group of linear transformations. It acts on the set $X=F_p^2$.
Then $C^X$ is a linear represintation of $G$. What is the decomposition of this represintation into irreducible represintations?

Note: Let $d_i$ number of isomorphic irreducible represintations. Then $\sum d_i^2$ equal to the number of orbits of $G$ when it acts on $X\otimes X$. The number of orbits of $G$ in $X\otimes X$ is $p+1$.