Let $\mathbb{F}_p$ be a finite field of order $p$ ($p$ prime) and $G=SL(2,7)$ be a special linear group of $2\times 2$ matrices over the field $\mathbb{F_7}.$ Let $\mathbb{F}_pG$ be the group ring (or group algebra). Let $$\Phi: \mathbb{F}_pG\to M_4(\mathbb{F}_p)$$ be an algebra homomorphism. Here $M_4(\mathbb{F}_p)$ is the set of all $4\times 4$ matrices.
Let $\mathbb{F}_pG$ be semisimple. This means that $p\neq 2, 3, 7$. Then I want to know the values of $p$ for which $\Phi$ can be onto.
I know that if $p=11$, then $\Phi$ can be onto but if $p=17$, then $\Phi$ can not be onto. How to show these? Is it related with the dimension of group algebra?
Please help me.