Modular polynomial of Hilbert:
- Gundlach invariants for sqrt(2) and l=2, 7, 17, 23, 31, 41, 47, 71 (split) and l=3, 5, 11 (inert);
- Gundlach invariants for sqrt(5) for l=5, 11, 19, 29, 31, 41, 59 (split) and for l=2, 3, 7 (inert);
- Theta invariants for sqrt(2): l= 7, 17, 23, 41, 73, 89, 97 (split) and for l= 3, 5, 11, 13 (inert)
- Theta invariants for sqrt(3) for l=13 (split) and for l=3, 5, 7 (inert)
- Theta invariants for sqrt(5) and for l=5, 11, 19, 29 , 31, 41, 59 (split) and for l=3, 7 (inert).
(To test the polynomials with the theta, you also need the files class-2, class-3, class-5 which contain the classes of the quotient SL_2(Ok\oplus\partial_K^{-1})/Gamma(2,4) for K=Q(sqrt(D)) and D=2,3,5 respectively.
Modular polynomial of Siegel:
You can find the code I wrote to compute the modular polynomials of Hilbert and of Siegel. The files lack of commentaries and explanations for now (sorry).