Mod-2 Hecke algebras of level 3 and 5

2022/07/31 by Shaunak V. Deo, Deo, Shaunak V., Anna Medvedovsky +1
Mathematics · #11F25 #11F33 #11F80 (primary) #20C08 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2208.00429

openalex publication_date 2022/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use deformation theory to study the big Hecke algebra acting on mod-2 modular forms of prime level N and all weights, especially its local component at the trivial representation. For N = 3, 5, we prove that the maximal reduced quotient of this big Hecke algebra is isomorphic to the maximal reduced quotient of the corresponding universal deformation ring. Then we completely determine the structure of this big Hecke algebra. We also describe a natural grading on mod-p Hecke algebras.

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