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arXiv · 1409.8342

Non-optimal levels of a reducible mod l modular representation

Hwajong Yoo
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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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Hwajong Yoo. 2014-09-29. Non-optimal levels of a reducible mod l modular representation. https://arxiv.org/abs/1409.8342

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