Timeline for Hecke operator which changes character
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May 18, 2019 at 19:59 | answer | added | Seewoo Lee | timeline score: 1 | |
Apr 17, 2017 at 9:02 | comment | added | Seewoo Lee | @DavidLoeffler I have no idea.. | |
Apr 17, 2017 at 7:47 | comment | added | David Loeffler | Do you know if the kernel of $\chi$ is a congruence subgroup? (I suspect it probably is not, which might explain why Hecke operators behave so differently here from the case studied by Miyake.) | |
Apr 17, 2017 at 3:36 | comment | added | Seewoo Lee | @reuns I added computation. | |
Apr 17, 2017 at 3:35 | history | edited | Seewoo Lee | CC BY-SA 3.0 |
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Apr 17, 2017 at 2:01 | comment | added | reuns | If $f(z)$ is modular for $\Gamma,\chi$ then $f(3z)$ is modular for ${\scriptstyle\begin{pmatrix}1&0\\0&1/3\end{pmatrix}}\Gamma{\scriptstyle\begin{pmatrix}1&0\\0&3\end{pmatrix}}, \tilde{\chi}$ where $\tilde{\chi}(\gamma) = \chi({\scriptstyle\begin{pmatrix}1&0\\0&3\end{pmatrix}}\gamma{\scriptstyle\begin{pmatrix}1&0\\0&1/3\end{pmatrix}})$. How do you treat the 3 other terms ? | |
Apr 16, 2017 at 8:39 | history | edited | Seewoo Lee | CC BY-SA 3.0 |
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Apr 16, 2017 at 8:13 | history | asked | Seewoo Lee | CC BY-SA 3.0 |