Timeline for Existence of Hecke operators with distinct eigenvalues?
Current License: CC BY-SA 3.0
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Jul 22, 2015 at 13:55 | comment | added | Kimball | @DavidLoeffler Thanks for the reference. I finally had time to look at it, but I don't quite see the connection. What they prove says that (say when N is squarefree) in each Galois conjugacy class the Fourier coefficients are distinct at a density 1 set of primes. But there can be many Galois orbits with the same coefficient field. Can you please clarify? | |
| Jul 4, 2015 at 15:16 | comment | added | David Loeffler | There is a paper by Koopa Koo, William Stein, and Gabor Wiese that is about exactly this question. | |
| Jul 4, 2015 at 4:39 | history | edited | Kimball | CC BY-SA 3.0 |
added edit
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| Jul 4, 2015 at 4:29 | comment | added | Kimball | @NoamD.Elkies Thanks. I was originally thinking of the weight 2 prime or squarefree level case, so I wasn't thinking about quadratic twists. Do you know what happens if you restrict to prime or squarefree level? | |
| Jul 4, 2015 at 2:54 | answer | added | FriendlyWendy | timeline score: 6 | |
| Jul 4, 2015 at 2:53 | comment | added | Noam D. Elkies | To construct a counterexample, use three forms $f_1,f_2,f_3$ in the same space (they can even be weight-2 newforms) that are quadratic twists of each other. For each $p$ at least two of the $f_i$ must have the same $T_p$ eigenvalue. | |
| Jul 4, 2015 at 2:29 | comment | added | Kimball | There is an (unanswered) question about this being true for any $p$ in level 1: mathoverflow.net/q/105713/6518 | |
| Jul 4, 2015 at 2:27 | history | asked | Kimball | CC BY-SA 3.0 |