Filtrations of dc-weak eigenforms

Nadim Rustom¹

¹ National Center for Theoretical Sciences National Taiwan University Room 203, Astronomy-Mathematics Building No. 1, Sec. 4, Roosevelt Rd. Taipei City 106, Taiwan

Acta Arithmetica, Tome 180 (2017) no. 4, pp. 297-318.

Résumé

The notions of strong, weak and dc-weak eigenforms mod $p^n$ were introduced and studied by Chen, Kiming and Wiese (2013). Here we prove that there can be no uniform weight bound (that is, depending only on $p,n$) on dc-weak eigenforms mod $p^n$ of fixed level when $n \geq 2$. This is in contrast with the result of Kiming, Rustom and Wiese (2016) which establishes a uniform weight bound on strong eigenforms mod $p^n$. As a step towards studying weight bounds for weak eigenforms mod $p^n$, we provide a criterion which allows us to detect whether a given dc-weak eigenform mod $p^n$ is weak.

Détail

DOI : 10.4064/aa8491-8-2017

Keywords: notions strong weak dc weak eigenforms mod introduced studied chen kiming wiese here prove there uniform weight bound depending only dc weak eigenforms mod fixed level geq contrast result kiming rustom wiese which establishes uniform weight bound strong eigenforms mod step towards studying weight bounds weak eigenforms mod provide criterion which allows detect whether given dc weak eigenform mod weak