Topological Modular Forms of Level 3

TL;DR

This paper computes the homotopy groups of topological modular forms spectra of level 3, focusing on level 3 structures at prime 2 and exploring connective models of TMF(Gamma_0(3)).

Contribution

It provides new computations of the homotopy groups for TMF spectra of level 3 and discusses models related to level 3 structures at prime 2.

Findings

Computed homotopy groups of TMF of level 3

Analyzed the building complex at prime 2

Identified connective models of TMF(Gamma_0(3))

Abstract

We describe and compute the homotopy of spectra of topological modular forms of level 3. We give some computations related to the "building complex" associated to level 3 structures at the prime 2. Finally, we note the existence of a number of connective models of the spectrum TMF(Gamma_0(3)).