When Ramanujan died in 1920, he left behind an incomplete, unpublished manuscript in two parts on the partition function p(n) and, in contemporary terminology, Ramanujan’s tau-function τ(n). The first part, beginning with the Roman numeral I, is written on 43 pages, with the last nine comprising material for insertion in the

Abstract. We prove that the parity of the partition function is given by the “trace ” of the Hauptmodul j ∗ 6(z) for Γ ∗ 0(6) at points of complex multiplication. Using Hecke operators, we generalize this to relate the Hecke traces of j ∗ 6(z) to the partition function modulo 2. We then prove that the generating function for these Hecke traces is equal to the logarithmic derivative of the level 6 Hilbert class polynomial. Finally, we give a procedure involving Hilbert class polynomials for computing the parity of the partition function, and make some speculations about the distribution of these universal polynomials modulo class polynomials.