Timeline for Hecke operators on universal elliptic curves
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 2, 2022 at 21:03 | comment | added | Will Sawin | @AdithyaChakravarthy In terms of $q$-expansions, I would find all the eigenforms, write a system of linear equations writing the differential as a sum of eigenforms, and solve. It may be possible to also do this using the Petersen inner product, taking advantage of the orthogonality of eigenforms to write the answer as the inner product of the differential with $f$, times $f$, divided by the inner product of $f$ with itself. | |
| Oct 2, 2022 at 20:17 | comment | added | Adithya Chakravarthy | I see. So given a differential on $E$, how would one go about computing its $f$-isotypical component? | |
| Oct 1, 2022 at 23:38 | comment | added | Will Sawin | @AdithyaChakravarthy I mean a presentation like yours where there is no change of variables for $x,y$ when $\tau$ is changed by an element of $\Gamma_1(N)$. | |
| Oct 1, 2022 at 23:25 | comment | added | Adithya Chakravarthy | Thanks for the very helpful answer! A clarification, what exactly do you mean by a "$\Gamma_1(N)$-invariant presentation of the universal family"? Explicitly, under what change of variables for $x,y$ would this presentation have to be invariant under? | |
| Oct 1, 2022 at 23:14 | vote | accept | Adithya Chakravarthy | ||
| Oct 1, 2022 at 23:13 | vote | accept | Adithya Chakravarthy | ||
| Oct 1, 2022 at 23:14 | |||||
| Oct 1, 2022 at 23:06 | history | answered | Will Sawin | CC BY-SA 4.0 |