An on-average Maeda-type conjecture 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 L -values (resp. L L -derivatives) are nonzero for 100 100% of even weight prime level newforms with root number + 1 +1 (resp. − 1 -1 ).