I should preface this by saying that I am not a representation theorist, so I apologize if this can easily be found in standard sources (but sadly I cannot seem to extract it from any of the books I know of).


Let $p$ be a prime number. What are all the irreducible representations (over $\mathbb{C}$) of $\text{SL}(n,\mathbb{F}\_p)$ and $\text{Sp}(2n,\mathbb{F}\_p)$ whose dimensions are $p^k$ for some $k$? There are the Steinberg representations, but I assume that there are also others.


I'm particularly interested in the symplectic group.



Representations of $\text{SL}(n,\mathbb{F}_p)$ and $\text{Sp}(2n,\mathbb{F}_p)$ whose dimensions are $p^k$
A full classification of such representations (and much more) can be found here:



> 
> *Prime power degree representations of
>  quasi-simple groups* by Malle and Zalesskii
> 
> 
> 


You can read this paper [here](http://www.uea.ac.uk//~h054/Malle-Z-2001.pdf). The main theorem implies that, apart from the Steinberg representation, there are no representations of this form. 


Interestingly this is not the case if you allow quasisimple covers of such groups, for instance $2\cdot {\rm Sp}\_6(2)$ has an irreducible complex representation of degree $2^9$.


As I mentioned in my comment, if you want to understand the theory of these representations then I would go to *Finite groups of Lie type* by Carter. I should also say that it's quite possible that the fact you seek can be proved more directly than via the full classification given by Malle and Zalesskii ... but I don't know enough of D-L theory to tell you how.


P.S. if anyone knows how to put the correct accent on Zalesskii's name, then I'd like to know how!


