Automorphic Forms on Feit's Hermitian Lattices. Issue 4 (1st December 2021)

• Record Type: Journal Article
• Authors: Dummigan, Neil; Schönnenbeck, Sebastian
• Is Part Of: Experimental mathematics. Volume 30:Issue 4(2021)
• Page Start: 557
• Page End: 574
• Publication Date: 2021-12-01
• Subjects: automorphic representations of unitary groups -- unimodular Hermitian lattices -- algebraic modular forms -- congruences of automorphic forms; 11F55 -- 11E39; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2019.1581857
• Languages: English
• ISSNs: 1058-6458

Abstract

Abstract: We consider the genus of 20 classes of unimodular Hermitian lattices of rank 12 over the Eisenstein integers. This set is the domain for a certain space of algebraic modular forms. We find a basis of Hecke eigenforms, and guess global Arthur parameters for the associated automorphic representations, which recover the computed Hecke eigenvalues. Congruences between Hecke eigenspaces, combined with the assumed parameters, recover known congruences for classical modular forms, and support new instances of conjectured Eisenstein congruences for U ( 2, 2 ) automorphic forms.