Timeline for Explicit Chebotarev density theorem for Galois representations associated to newforms
Current License: CC BY-SA 4.0
7 events
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| May 10, 2022 at 13:41 | vote | accept | CommunityBot | ||
| May 6, 2022 at 15:08 | answer | added | 2734364041 | timeline score: 0 | |
| Apr 12, 2022 at 9:51 | history | edited | user471019 | CC BY-SA 4.0 |
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| Apr 10, 2022 at 14:48 | history | edited | LSpice | CC BY-SA 4.0 |
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| Apr 10, 2022 at 14:43 | comment | added | user471019 | Thanks. Two questions: 1. What is the best known Chebotarev density estimate? 2. Are there better bounds exploiting the fact that $\rho$ is modular? I'm looking for bounds $M$ which one could actually check using a computer. | |
| Apr 10, 2022 at 13:57 | comment | added | Ariel Weiss | The representation $\rho$ factors through a finite Galois extension $\mathrm{Gal}(L_f/\mathbb Q)$. The field $L_f$ is unramified outside $Np$ and has degree at most $|\mathrm{GL}_2(\mathbb F)|$ (actually, it's a bit smaller - there are constraints coming from the determinant). So by Hermite-Minkowski, every Galois representation of this shape factors through some $\mathrm{Gal}(L/\mathbb Q)$ where now $L$ depends only on $N$, $p$ and the size of $\mathbb F$. All this can be made explicit, and now you can just apply standard Chebotarev estimates to the extension $L/\mathbb Q$. | |
| Apr 10, 2022 at 13:49 | history | asked | user471019 | CC BY-SA 4.0 |