Irreducible representations of modular group $SL(2,Z)$ with finite image

Question

The classification of irreducible representations of modular group $SL(2,Z)$ is difficult. But for the representations with finite image (the 1-dimensional representation is simple, with only 12), the 2-dimensional case is well established, with only 54 non-equivalent irreducible representations (G.Mason 2008). What I want to ask is, are also there only finite irreducible representations with finite image in 3-dimensional cases and above?