Base field \(\Q(\sqrt{133}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 33\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[23,23,w - 8]$ |
Dimension: | $32$ |
CM: | no |
Base change: | no |
Newspace dimension: | $58$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{32} - 57x^{30} + 1449x^{28} - 21799x^{26} + 217073x^{24} - 1515157x^{22} + 7651945x^{20} - 28431874x^{18} + 78198752x^{16} - 158750660x^{14} + 235127148x^{12} - 248703032x^{10} + 181751760x^{8} - 87469376x^{6} + 25852512x^{4} - 4156416x^{2} + 270848\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w + 6]$ | $\phantom{-}e$ |
3 | $[3, 3, -w - 5]$ | $...$ |
4 | $[4, 2, 2]$ | $...$ |
7 | $[7, 7, 3w - 19]$ | $...$ |
11 | $[11, 11, -2w - 11]$ | $...$ |
11 | $[11, 11, -2w + 13]$ | $...$ |
13 | $[13, 13, w + 4]$ | $...$ |
13 | $[13, 13, -w + 5]$ | $...$ |
19 | $[19, 19, 5w - 31]$ | $...$ |
23 | $[23, 23, -w - 7]$ | $...$ |
23 | $[23, 23, w - 8]$ | $-1$ |
25 | $[25, 5, -5]$ | $...$ |
31 | $[31, 31, -w - 1]$ | $...$ |
31 | $[31, 31, w - 2]$ | $...$ |
41 | $[41, 41, 6w + 31]$ | $...$ |
41 | $[41, 41, 6w - 37]$ | $...$ |
43 | $[43, 43, -3w - 17]$ | $...$ |
43 | $[43, 43, -3w + 20]$ | $...$ |
59 | $[59, 59, 3w - 17]$ | $...$ |
59 | $[59, 59, 3w + 14]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$23$ | $[23,23,w - 8]$ | $1$ |