Abstract
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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Acknowledgement
First named author partially supported by grant MTM2012-33830 and by an ICREA Academia prize, second by DGICYT Grant MTM2009-11068.
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The three authors have contributed to this work in equal parts. All authors read and approved the final manuscript.
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Dieulefait, L.V., Urroz, J.J. & Ribet, K.A. Modular forms with large coefficient fields via congruences. Res. number theory 1, 2 (2015). https://doi.org/10.1007/s40993-015-0003-9
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DOI: https://doi.org/10.1007/s40993-015-0003-9
Keywords
- Modular Form
- Elliptic Curf
- Diophantine Equation
- Galois Representation
- Multiplicative Function