Example of a finite dimensional algebra over $C$ with a simple module of dimension $2013$

Question

What is an example of a finite dimensional algebra $A$ over $\mathbb{C}$ with a simple module of dimension $2013$?

I don't know if the general case holds here (there exists $A$ and a simple module of dimension $n$) or if there is a specific example for $2013$.

My first idea was a group algebra, something like $\mathbb{C}C_{2013k}$, but this is a commutative algebra so all simple modules will be one-dimensional.

Answer 1

HINT:

You can make it a group algebra: $S_n$ has an irreducible representation of dimension $n-1$.