Timeline for Conductor of monomial forms with trivial nebentypus
Current License: CC BY-SA 2.5
12 events
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| Mar 9, 2010 at 10:26 | answer | added | Kevin Buzzard | timeline score: 6 | |
| Mar 8, 2010 at 20:51 | comment | added | Kevin Buzzard | Is this a p-adic or a complex representation? I am envisaging the 2-adic Tate module of X_0(32), which is "dihedral" for some values of dihedral, and has "conductor 1" for some values of conductor. But apart from what, read what Emerton said about the Steinberg: it's the only smooth irred rep of GL_2(Q_p) of conductor p and with unramified central character, and it can't show up for global reasons, so if you have trivial det you can't have p dividing the conductor eactly once in a dihedral setting. | |
| Mar 8, 2010 at 17:02 | comment | added | Idoneal | Sorry. I was too careless in phrasing the question. There are certainly many dihedral forms of prime conductors. I forgot to add the condition that I believe should give the desired conclusion. I have modified the question. | |
| Mar 8, 2010 at 16:54 | history | edited | Idoneal | CC BY-SA 2.5 |
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| Mar 8, 2010 at 16:48 | history | edited | Idoneal | CC BY-SA 2.5 |
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| Mar 8, 2010 at 16:27 | answer | added | Emerton | timeline score: 4 | |
| Mar 8, 2010 at 13:28 | comment | added | Kevin Buzzard | There's a weight 1 cuspidal modular form of level 23, whose associated Galois representation is induced from an unramified character of Q(sqrt(-23)). OK so I really give in now ;-) | |
| Mar 8, 2010 at 13:14 | comment | added | Kevin Buzzard | A Dirichlet character is monomial and can have prime conductor. I think your question is too terse/ambiguous currently. | |
| Mar 8, 2010 at 12:03 | comment | added | Kevin Buzzard | The conductor could be 1, right? Isn't that squarefree? Are you talking about 2-dimensional representations? Of an arbitrary number field? | |
| Mar 8, 2010 at 11:35 | history | edited | Idoneal | CC BY-SA 2.5 |
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| Mar 8, 2010 at 11:26 | history | edited | Tom Leinster |
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| Mar 8, 2010 at 11:16 | history | asked | Idoneal | CC BY-SA 2.5 |