Timeline for What is the image of the Hecke operator $U_p$?
Current License: CC BY-SA 4.0
8 events
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| May 11, 2023 at 14:51 | comment | added | David Loeffler | Looking back at this over breakfast, I realised that the title of Adithya's post raises a slightly more refined question than the body of the question -- identifying the exact image of $U_p$. So for good measure I have edited my post to answer this as well. | |
| May 11, 2023 at 3:06 | vote | accept | Adithya Chakravarthy | ||
| May 11, 2023 at 2:27 | comment | added | GH from MO | @DavidLoeffler Thanks for clarifying this. Indeed, the quoted theorem talks about the image (or Hecke eigenvalue) of a newform. In representation theoretic language, the corresponding local representation is supercuspidal. | |
| May 10, 2023 at 23:10 | comment | added | David Loeffler | ... and you can also find at that source that "Theorem 5 of Atkin-Lehner" does not contain the claimed statement. Which is fortunate, since the statement is actually false; see my answer below. | |
| May 10, 2023 at 23:08 | answer | added | David Loeffler | timeline score: 4 | |
| May 10, 2023 at 22:22 | comment | added | GH from MO | You can find "Theorem 5 of Atkin-Lehner" here: gdz.sub.uni-goettingen.de/id/… | |
| May 10, 2023 at 20:56 | comment | added | Kimball | See Theorem 5 of Atkin-Lehner. | |
| May 10, 2023 at 17:52 | history | asked | Adithya Chakravarthy | CC BY-SA 4.0 |