The beta family at the prime two and modular forms of level three

TL;DR

This paper explores the relationship between the beta family at prime 2 and modular forms of level three, using elliptic genus techniques to compute f-invariants within the ring of divided congruences.

Contribution

It introduces an elliptic Greek letter beta construction that maps the beta family into modular forms, providing explicit calculations of f-invariants at prime 2.

Findings

Mapping of the beta family into the ring of divided congruences

Explicit computation of f-invariants for the beta family

Application of elliptic genus techniques to modular forms

Abstract

We use the orientation underlying the Hirzebruch genus of level three to map the beta family at the prime p=2 into the ring of divided congruences. This procedure, which may be thought of as the elliptic greek letter beta construction, yields the f-invariants of this family.