Books on modular forms don't usually attribute the main results to anyone. For instance, who first obtained that values of the $j$ invariant at quadratic imaginary points (singular moduli) are algebraic integers?
More generally, is there a good source for historical accounts on the arithmetic theory of modular forms?
This goes back to Kronecker. See "Kronecker's Jugendtraum and Modular Functions" by Vladut.
Also see the first two sections here, the second section here, and Sections 1, 3, and 4 here.