Explicit modular forms from the divided beta family

TL;DR

This paper computes specific modular forms linked to the order 5 generators in the 5-local Adams-Novikov spectral sequence, extending previous work and proposing conjectures for similar forms at larger primes.

Contribution

It generalizes previous computations of modular forms from the divided beta family and conjectures formulas for these forms at arbitrary primes ≥ 5.

Findings

Explicit computations of modular forms at prime 5

Analogous computations at other primes

Conjectured formulas for modular forms at primes ≥ 5

Abstract

We compute modular forms known to arise from the order 5 generators of the 5-local Adams-Novikov spectral sequence 2-line, generalizing and contextualizing previous computations of M. Behrens and G. Laures. We exhibit analogous computations at other primes and conjecture formulas for some of the modular forms arising in this way at arbitrary primes greater than or equal to 5.