Timeline for Explicit computation of the effect of the Atkin-Lehner operator/Fricke involution's effect on $q$-expansion
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 9, 2021 at 10:16 | comment | added | David Loeffler | Here you go: warwick.ac.uk/fac/sci/maths/people/staff/david_loeffler/… | |
| Nov 9, 2021 at 8:13 | comment | added | Garrett Credi | @DavidLoeffler If you would feel comfortable doing so, I would greatly appreciate it! | |
| Nov 8, 2021 at 7:47 | comment | added | David Loeffler | @GarrettCredi This isn't implemented in the Sage library. I have some experimental code of my own which I could share, but it is very slow. | |
| Nov 7, 2021 at 17:36 | comment | added | Garrett Credi | @DavidLoeffler Do you know of any way for Sage to compute the action of Atkin-Lehner on non-newforms? | |
| Nov 7, 2021 at 15:36 | vote | accept | Garrett Credi | ||
| Nov 7, 2021 at 15:19 | comment | added | François Brunault | @David Thank you for adding these informations about the Sage implementation. I wanted to mention that there was very probably one, but I didn't know the details. For weight 1, I think Pari simply multiplies by a suitable power of a theta function, and applies Borisov-Gunnells to the result. | |
| Nov 7, 2021 at 15:11 | comment | added | David Loeffler | Just as a footnote to this excellent answer: as well as the Magma and Pari implementations which Francois mentions, there is also code in Sage for computing the action of Atkin-Lehner on newforms. Unlike Magma, this works for all levels and characters (although not for weight 1); unlike Pari, it is a completely algebraic algorithm based on modular symbols, so there are no inexact approximations involved and its results are provably correct (modulo bugs). | |
| Nov 7, 2021 at 12:06 | history | answered | François Brunault | CC BY-SA 4.0 |