The group $\text{SL}(2,\mathbb{Z})$ is the group of two-by-two matrices with integer entries and determinant one. This is a very simple definition. Yet its representation theory seems quite wild to me (a PhD physics student) from the limited information I can find online... In particular, it seems it has uncountably many irreducible representations. I am also aware that if we restrict ourselves to the class of representations with finite image and whose kernel can be described by congruences, the representation theory becomes way more well-behaved. These are the so-called congruence subgroups.

I would like to learn more about the representation theory of $\text{SL}(2,\mathbb{Z})$ beyond the classical textbook discussions restricted on congruence subgroups.

Any good general references (papers, book, ...) I could look into?