On the slopes of the {U_5} operator acting on overconvergent modular forms | Zendy

L. J. P. Kilford | Zendy

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On the slopes of the {U_5} operator acting on overconvergent modular forms

Author(s) -

L. J. P. Kilford

Publication year - 2008

Publication title -

journal de théorie des nombres de bordeaux

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.663

H-Index - 26

eISSN - 2118-8572

pISSN - 1246-7405

DOI - 10.5802/jtnb.620

Subject(s) - mathematics , modular form , operator (biology) , modular design , pure mathematics , character (mathematics) , conductor , number theory , dirichlet distribution , algebra over a field , mathematical analysis , geometry , computer science , biochemistry , chemistry , repressor , transcription factor , gene , boundary value problem , operating system

We show that the slopes of the~$U_5$ operator acting on slopes of 5-adic overconvergent modular forms of weight~$k$ with primitive Dirichlet character~$\chi$ of conductor~25 are given by either \[ \left\{{1/4}\cdot\lfloor\frac{8i}{5}\rfloor: i \in \N\right\}\text{or }\left\{{1/4}\cdot\lfloor\frac{8i+4}{5}\rfloor: i \in \N\right\}, \] depending on~$k$ and~$\chi$.

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