We study skeins on the 2-torus and 3-torus via the representation theory of the double affine Hecke algebra of type A and its connection to quantum D-modules. As an application we can compute the dimension of the generic $\operatorname{SL}_N$- and $\operatorname{GL}_N$-skein module of the 3-torus for arbitrary $N$. This is joint work with Sam Gunningham and David Jordan.