$(2+)$-Replication and the Baby Monster

The definitions of replicable and completely replicable functions are intimately related to the Hecke operators for the modular group. We define the notions of "$(2+)$-replicable" and "completely $(2+)$-replicable" functions by considering the Hecke operators for $\Gamma_0(2)^+$. We prove that the McKay–Thompson series for $2\cdot\mathbb{B}$, as computed by Höhn, are completely $(2+)$-replicable.