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.
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2015 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/81139 |
| Online Access: | https://hdl.handle.net/2117/81139 https://dx.doi.org/10.1007/s40993-015-0003-9 |
| Access Level: | Open access |
| Keyword: | Numerical analysis Anàlisi numèrica Classificació AMS::65 Numerical analysis::65L Ordinary differential equations Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics |
| Summary: | 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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