On Drinfeld cusp forms of prime level

2019/08/26 by Andrea Bandini, Bandini, Andrea, Maria Valentino +1
Mathematics · #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.1908.09768

openalex publication_date 2019/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (P_d) be any prime of \mathbbF_q[t] of degree d and consider the space of Drinfeld cusp forms of level P_d, i.e. for the modular group Γ₀(P_d). We provide a definition for oldforms and newforms of level P_d. Moreover, when the dimension of the vector space of oldforms is one and P₁=t we prove that the space of cuspforms of level t is the direct sum of oldforms and newforms and that the Hecke operator T_t acting on Drinfeld cusp forms of level 1 is injective, thus providing more evidence for the conjectures presented and stated in [2] and [3].

Related

• Traces of Hecke operators on Drinfeld modular forms for \mathbbF_q[T]
• Hecke Operators on Drinfeld Cusp Forms
• A Hecke-equivariant decomposition of spaces of Drinfeld cusp forms via representation theory, and an investigation of its subfactors
• Triviality of the Hecke action on ordinary Drinfeld cuspforms of level Γ₁(tⁿ)
• On Drinfeld modular forms of higher rank IV: Modular forms with level