Timeline for Weight 3 modular form associated to singular abelian surfaces?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 10, 2020 at 1:00 | comment | added | Benighted | @DavidLoeffler Is there something in the literature which covers what I'm asking about? Ideally, I'd like to be able to look these weight 3 forms up, if it's that easy. | |
| Mar 9, 2020 at 10:03 | comment | added | Donu Arapura | Yes, sorry I was a bit hasty, I meant a subquotient of $S^2H^1(E)$ | |
| Mar 9, 2020 at 7:08 | comment | added | David Loeffler | There is $\epsilon$ more to this, because if $E$ is CM, then $S^2 H^1(E)$ is reducible. $H^1(E)$ is the induction of a 1-diml representation $\psi$ of $G_K$, where $K$ is the CM field, and $S^2 H^1(E)$ splits as (cyclo char) + (induction of $\psi^2$) and the induction of $\psi^2$ corresponds to a wt 3 mod form. | |
| Mar 9, 2020 at 0:59 | comment | added | Benighted | Interesting, I didn't know about this nice connection to extremal K3s. Thanks! So you're expecting that the modular form for $A$ and it's Kummer K3 should be the same? Also, do you mind if I clarify what you mean by $S^{2}$? I was guessing symmetric product, but I thought we wanted specifically 2-dimensional Galois representations. | |
| Mar 8, 2020 at 22:30 | history | answered | Donu Arapura | CC BY-SA 4.0 |