Timeline for Integrality of Atkin-Lehner operator for $\Gamma_1(N)$
Current License: CC BY-SA 4.0
4 events
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| Apr 8, 2020 at 6:50 | comment | added | David Loeffler | If you're working with $\Gamma_0(N) \cap \Gamma_1(M)$ (i.e. level $N$ and characters of conductor dividing $M$) then the exact same argument shows $w_Q$ is defined over $\mathbf{Z}[1/N, \zeta_d]$ where $d = GCD(M, Q)$. (But this isn't really an "integrality" result as such, because the $1/N$ is still there, it's just controlling the roots of unity a little better.) | |
| Apr 8, 2020 at 0:47 | comment | added | Daniel Johnston | Thank you very much, this is very useful! Do you know whether there is an even simpler integrality statement if we instead restrict to modular forms with character? That is, would the Atkin-Lehner operator $w_{Q,k}$ be $\mathbb{Z}[1/N,\zeta_d]$-integral for some $d$ related to the conductor of the character? If there isn't a clear answer to this I'm happy to make a new question. | |
| Mar 9, 2020 at 10:17 | vote | accept | Daniel Johnston | ||
| Mar 9, 2020 at 8:52 | history | answered | David Loeffler | CC BY-SA 4.0 |