  We propose to generalize the work of R\'egis Dupont for computing modular
polynomials in dimension $2$ to new invariants. We describe an algorithm to
compute modular polynomials for invariants derived from theta constants and
prove under some heuristics that this algorithm is quasi-linear in its output
size. Some properties of the modular polynomials defined from quotients of
theta constants are analyzed. We report on experiments with our implementation.
