Relations between higher level Hurwitz class numbers

Abstract: We connect generalizations of the classical Hurwitz class numbers coming from two different frameworks: one introduced by Pei and Wang, arising from the generalized Cohen-Eisenstein series, and another by Li, Skoruppa, and Zhou, arising from Eichler orders of quaternion algebras. As applications, we obtain new structural results, a generalization of recent results of Beckwith and Mono, and a generalization of Gauss' formula.