An on-average Maeda-type conjecture in the level aspect

TL;DR

This paper proposes a conjecture about the average number of Galois orbits of newforms at fixed weight while varying level, with implications for the nonvanishing of central L-values and derivatives.

Contribution

It introduces a new conjecture relating Galois orbits of newforms to level variation, extending Maeda-type conjectures to the level aspect.

Findings

Conjecture predicts 100% nonvanishing of central L-values for certain newforms.

Implication for the distribution of Galois orbits in modular forms.

Provides a new perspective on the behavior of L-functions in the level aspect.

Abstract

We present a conjecture on the average number of Galois orbits of newforms when fixing the weight and varying the level. This conjecture implies, for instance, that the central L-values (resp. L-derivatives) are nonzero for 100% of even weight prime level newforms with root number +1 (resp. -1).