Timeline for Counterexamples for (weak) multiplicity one
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 7, 2013 at 9:09 | vote | accept | Fabian Werner | ||
| Mar 6, 2013 at 17:03 | comment | added | Marc Palm | But there is nothing wrong about your statement (except perhapas that for neglecting ramified Hecke operators you can't really refer to weak multiplicity one). I was just curious;) | |
| Mar 6, 2013 at 16:57 | comment | added | Marc Palm | T(m) at m dividing N doesn't give you something very useful. You need to change the operator at m dividing the level. There are ramified and unramified Hecke operators. Of course, the statement will hold as well, but because of knowing the Hecke eigenvalue at almost all primes determines... T(m) (as originally defined) is identically zero on newforms for m|N. | |
| Mar 6, 2013 at 16:44 | comment | added | Fabian Werner | Wait, what? Do we talk about two different Hecke algebras maybe? I mean the one generated by all the $T(m)$ where $m$ runs through the natural numbers (lets say we consider the abstract sums of double cosets, not even the operators on modular forms). This Hecke algebra is commutative and hence their induced operator-algebra is commutative on the whole space $M_k(\Gamma_0(N))$. Do i still misunderstand something? | |
| Mar 6, 2013 at 16:30 | comment | added | Marc Palm | But become commutative algebra only when restricted to newforms (Atkin-Lehner). So the question is rather, how do diagonalize the family of Hecke operators (necessary for finding joint eigenfunctions) if you do not consider newforms? | |
| Mar 6, 2013 at 16:25 | comment | added | GH from MO | Fabian, read my response. | |
| Mar 6, 2013 at 16:23 | comment | added | Fabian Werner | I do not understand the question: Hecke operators are defined on the space $M_k(\Gamma_0(N))$ and oldforms are elements of that space... | |
| Mar 6, 2013 at 16:20 | answer | added | GH from MO | timeline score: 5 | |
| Mar 6, 2013 at 16:16 | comment | added | Marc Palm | How do you define Hecke operators on old forms? | |
| Mar 6, 2013 at 16:10 | answer | added | Marc Palm | timeline score: 1 | |
| Mar 6, 2013 at 15:39 | history | asked | Fabian Werner | CC BY-SA 3.0 |