We use the orientation underlying the Hirzebruch genus of level three to map the beta family at the prime into the ring of divided congruences. This procedure, which may be thought of as the elliptic Greek letter beta construction, yields the –invariants of this family.
"The beta family at the prime two and modular forms of level three." Algebr. Geom. Topol. 16 (5) 2851 - 2864, 2016. https://doi.org/10.2140/agt.2016.16.2851