Timeline for Level lowering for weight 1 forms
Current License: CC BY-SA 3.0
5 events
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| Oct 19, 2012 at 9:53 | comment | added | jnewton | Dear Robert, if you assume that $a_p(f)^2 \ne \chi(p)$ mod $p$ then I think you can deduce level lowering in weight one from level lowering in weight $p$ using Corollary 13.11 of Gross's companion forms paper. At least, this will give you a mod $p$ weight one form of level $N/q$ - I don't know how easy it is to show that this form will lift to characteristic zero when the form of level $N$ you started with lifts, which seems to be the setting of your question. The weight one case of Gross's result was generalised to the Hilbert setting recently by Gee and Kassaei (arXiv:1206.6631). | |
| Oct 19, 2012 at 2:25 | comment | added | Filippo Alberto Edoardo | In math.ubc.ca/~vatsal/research/pseudo.pdf Cho and Vatsal study the behavior of specialization of Hida families in weight one from a deformation perspective (in a paper with Ghate, Vatsal said it was being done with Greenberg, but the paper did not appear). Relying on that, can't you deduce your result from the analogous in weight bigger than $1$ - I guess you tried, what goes wrong? | |
| Oct 18, 2012 at 18:03 | answer | added | Olivier | timeline score: 2 | |
| Oct 18, 2012 at 17:07 | comment | added | Marc Palm | I am not trained in Galois representations. Will the level lowering have the same factorization as automorphic representation? If yes, it might be easier to analyze which invariant vectors the representation at $q$ has? What is the conductor of $\chi$ btw? | |
| Oct 18, 2012 at 17:01 | history | asked | sibilant | CC BY-SA 3.0 |