A possible generalization of Maeda's conjecture

TL;DR

This paper presents computational observations suggesting a generalization of Maeda's conjecture to higher levels, proposing a potential formula for the number of Galois orbits of newforms.

Contribution

It introduces a conjectural extension of Maeda's conjecture to higher levels and offers a possible formula for counting Galois orbits of newforms.

Findings

Computational data supports the generalization hypothesis.

A potential formula for the number of Galois orbits is proposed.

Observations suggest patterns in the distribution of newforms at higher levels.

Abstract

We report on observations we made on computational data that suggest a generalization of Maeda's conjecture regarding the number of Galois orbits of newforms of level $N = 1$, to higher levels. They also suggest a possible formula for this number in many of these cases.