Modular forms with large coefficient fields via congruences

We use the theory of congruences between modular forms to prove the existence of newforms with square-free level having a fixed number of prime factors such that the degree of their coefficient fields is arbitrarily large. We also prove a similar result for certain almost square-free levels.

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Veröffentlicht in:	Research in number theory 2015-12, Vol.1 (1), Article 2
Hauptverfasser:	Dieulefait, Luis Víctor, Urroz, Jorge Jiménez, Ribet, Kenneth Alan
Format:	Artikel
Sprache:	eng
Schlagworte:	65 Numerical analysis 65L Ordinary differential equations Anàlisi numèrica Classificació AMS Matemàtiques i estadística Mathematics Mathematics and Statistics Mètodes numèrics Number Theory Numerical analysis Research Article Àrees temàtiques de la UPC
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Beschreibung
Zusammenfassung:	We use the theory of congruences between modular forms to prove the existence of newforms with square-free level having a fixed number of prime factors such that the degree of their coefficient fields is arbitrarily large. We also prove a similar result for certain almost square-free levels.
ISSN:	2363-9555 2363-9555
DOI:	10.1007/s40993-015-0003-9