Newforms mod p in squarefree level, with applications to Monsky's\n Hecke-stable filtration

2018/08/14 by Shaunak V. Deo, Deo, Shaunak V., Anna Medvedovsky +3
Mathematics · #11F11 #11F23 (Secondary) #11F25 #11F33 (Primary) 11F30 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1808.04588

openalex publication_date 2018/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose an algebraic definition of the space of l-new mod-p modular forms\nfor Gamma0(Nl) in the case that l is prime to N, which naturally generalizes to\na notion of newforms modulo p in squarefree level. We use this notion of\nnewforms to interpret the Hecke algebras on the graded pieces of the space of\nmod-2 level-3 modular forms described by Paul Monsky. Along the way, we\ndescribe a renormalized version of the Atkin-Lehner involution: no longer an\ninvolution, it is an automorphism of the algebra of modular forms, even in\ncharacteristic p.\n

Related

• Defining newforms in characteristic p
• Images of Pseudo-Representations and Coefficients of Modular Forms modulo p
• Decomposition theorems for Hilbert modular newforms
• On mod p modular representations which are defined over \F_p
• Hecke stability and weight 1 modular forms