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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Non-optimal levels of a reducible mod $\ell$ modular representation
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by Hwajong Yoo PDF
Trans. Amer. Math. Soc. 371 (2019), 3805-3830 Request permission

Abstract:

Let $\ell \geq 5$ be a prime and let $N$ be a square-free integer prime to $\ell$. For each prime $p$ dividing $N$, let $a_p$ be either $1$ or $-1$. We give sufficient criteria for the existence of a newform $f$ of weight 2 for $\Gamma _0(N)$ such that the mod $\ell$ Galois representation attached to $f$ is reducible and $U_p f = a_p f$ for primes $p$ dividing $N$. The main techniques used are level raising methods based on an exact sequence due to Ribet.
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Additional Information
  • Hwajong Yoo
  • Affiliation: Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang, Republic of Korea 37673
  • Address at time of publication: College of Liberal Studies, Seoul National University 1 Gwanak-ro, Gwanak-gu, Seoul 08826, South Korea
  • MR Author ID: 1146780
  • Email: hwajong@gmail.com
  • Received by editor(s): May 26, 2016
  • Received by editor(s) in revised form: June 15, 2017, and June 21, 2017
  • Published electronically: November 16, 2018
  • Additional Notes: This work was supported by IBS-R003-D1.
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 371 (2019), 3805-3830
  • MSC (2010): Primary 11F33, 11F80; Secondary 11G18
  • DOI: https://doi.org/10.1090/tran/7314
  • MathSciNet review: 3917209