In the recent paper by Ono and Bruinier (it's currently on the AIM web site) "An algebraic formula for the partition function" they use their formula to determine the number of partitions of 1.
This calculation involves CM points, evaluating a certain week Maasweak Maass form at these points, the Hilbert class field of $\mathbb{Q}(\sqrt{-23})$, ... etc.