A remark on dimensions of spaces of modular forms
type: Item
instance of: scholarly article
title: A remark on dimensions of spaces of modular forms
zbMATH Open document ID: 0860.11020
DOI: 10.1007/BF01194172
author: Ernst-Ulrich Gekeler
published in: Archiv der Mathematik
publication date: 1997-04-24T00:00:00Z
review text: Let \(k,N\in \mathbb{N},k\) even, \(N\) squarefree. Denote by \(S_k(N)\) the space of elliptic cusp forms of weight \(k\) on \(\Gamma_0(N)\). Let \(S^*_k(N)\) be its semi-simple part, i.e. the largest submodule of \(S_k(N)\) on which the algebra generated by the Hecke operators \(T_p\), \(p\) prime, acts semi-simply. The author derives an explicit formula for \(\dim S^*_k(N)\), which surprisingly does not involve the prime decomposition of \(N\). As a corollary he obtains \[ \dim S^*_{k+12} (N)=1 + \dim S^*_k(N) \quad \text{for} \quad (k,N) \neq(2,1). \]
Mathematics Subject Classification ID: 11F11
zbMATH DE Number: 937048
zbMATH Keywords: dimension formula
zbMATH Keywords: space of elliptic cusp forms
zbMATH Keywords: semi-simple
zbMATH Keywords: Hecke operators
reviewed by: Aloys Krieg
MaRDI profile type: Publication
cites work: Q5672700
cites work: Jacobians of Drinfeld modular curves.
cites work: FUNDAMENTAL DOMAINS OF SOME ARITHMETIC GROUPS OVER FUNCTION FIELDS
cites work: Automorphic Forms on Adele Groups. (AM-83)
cites work: Q5625265
description: scientific article; zbMATH DE number 937048