I was learning about the representation of $\operatorname{GL}_2$ over local fields and came to know something like: if the residual characteristic of the local field is an odd prime, then every supercuspidal representation is a dihedral supercuspidal representation. I know what is a dihedral supercuspidal representation (I read it in Bump's Automorphic forms book).

But I could not find the previous statement when residual characteristic is odd. Please suggest some good references for this.

From the first two lines it is pretty clear that if the residual characteristic of the local field is even, then there are non-dihedral supercuspidal representations. I also want to know about them. Please suggest some references for this too.