Slopes of 2-adic overvconvergent modular forms with small level

LJP Kilford

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

Let~$\tau$ be the primitive Dirichlet character of conductor~$4$, let~$\chi$ be the primitive even Dirichlet character of conductor~$8$ and let~$k$ be an integer. We show that the~$U_2$ operator acting on cuspidal overconvergent modular forms of weight~$2k-1$ and character~$\tau$ has slopes in the arithmetic progression\\~$\left\{2,4,\ldots,2n,\ldots\right\}$, and the~$U_2$ operator acting on cuspidal overconvergent modular forms of weight~$k$ and character~$\chi \cdot \tau^k$ has slopes in the arithmetic progression~$\left\{1,2,\ldots,n,\ldots\right\}$. We also show that the characteristic polynomials of the Hecke operators~$U_2$ and~$T_p$ acting on the space of classical cusp forms of weight~$k$ and character either~$\tau$ or~$\chi\cdot\tau^k$ split completely over~$\mathbf{Q}_2$.
Translated title of the contributionSlopes of 2-adic overvconvergent modular forms with small level
Original languageEnglish
Pages (from-to)723 - 739
Number of pages17
JournalMathematics Research Letters
Volume11 (6)
Publication statusPublished - Nov 2004

Fingerprint Dive into the research topics of 'Slopes of 2-adic overvconvergent modular forms with small level'. Together they form a unique fingerprint.

Cite this