  Recently, Bruinier and Ono found an algebraic formula for the partition
function in terms of traces of singular moduli of a certain non-holomorphic
modular function. In this paper we prove that the rational polynomial having
these singuar moduli as zeros is (essentially) irreducible, settling a question
of Bruinier and Ono. The proof uses careful analytic estimates together with
some related work of Dewar and Murty, as well as extensive numerical
calculations of Sutherland.
