N=4 characters in Gepner models, orbits and elliptic genera

We review the properties of characters of the N=4 superconformal algebra in the context of a nonlinear sigma model on K3, how they are used to span the orbits, and how the orbits produce topological invariants like the elliptic genus. We derive the same expression for the K3 elliptic genus using three different Gepner models (16, 24, and 43 theories), detailing the orbits and verifying that their coefficients Fi are given by elementary modular functions. We also reveal the orbits for the 1322, 144, and 1242 theories. We derive relations for cubes of theta functions and study the function (1/η) ΣnisamemberofZ(-1)n(6n+1)k q(6n+1)2/24 for k=1,2,3,4