Base field 3.3.1257.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 9\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[13, 13, w + 2]$ |
Dimension: | $10$ |
CM: | no |
Base change: | no |
Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} - 19x^{8} + 112x^{6} - 264x^{4} + 243x^{2} - 72\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w + 3]$ | $-\frac{5}{51}e^{8} + \frac{91}{51}e^{6} - \frac{159}{17}e^{4} + 16e^{2} - \frac{116}{17}$ |
3 | $[3, 3, w - 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w^{2} + w - 5]$ | $-\frac{2}{17}e^{9} + \frac{116}{51}e^{7} - \frac{688}{51}e^{5} + 29e^{3} - \frac{299}{17}e$ |
8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{17}e^{8} - \frac{58}{51}e^{6} + \frac{344}{51}e^{4} - 15e^{2} + \frac{141}{17}$ |
13 | $[13, 13, w + 2]$ | $-1$ |
13 | $[13, 13, -2w + 5]$ | $\phantom{-}\frac{8}{51}e^{9} - \frac{149}{51}e^{7} + \frac{821}{51}e^{5} - 30e^{3} + \frac{206}{17}e$ |
13 | $[13, 13, -w^{2} - w + 4]$ | $-\frac{8}{51}e^{9} + \frac{149}{51}e^{7} - \frac{821}{51}e^{5} + 30e^{3} - \frac{206}{17}e$ |
19 | $[19, 19, -w^{2} + w + 4]$ | $\phantom{-}\frac{22}{51}e^{9} - \frac{397}{51}e^{7} + \frac{2092}{51}e^{5} - 77e^{3} + \frac{660}{17}e$ |
23 | $[23, 23, -w^{2} - w + 7]$ | $\phantom{-}\frac{2}{51}e^{9} - \frac{11}{17}e^{7} + \frac{133}{51}e^{5} - e^{3} - \frac{76}{17}e$ |
25 | $[25, 5, w^{2} - 2w - 1]$ | $-\frac{13}{51}e^{9} + \frac{223}{51}e^{7} - \frac{1060}{51}e^{5} + 33e^{3} - \frac{186}{17}e$ |
29 | $[29, 29, w^{2} - 5]$ | $\phantom{-}\frac{16}{51}e^{9} - \frac{281}{51}e^{7} + \frac{468}{17}e^{5} - 48e^{3} + \frac{378}{17}e$ |
31 | $[31, 31, w^{2} + w - 8]$ | $\phantom{-}\frac{3}{17}e^{9} - \frac{58}{17}e^{7} + \frac{344}{17}e^{5} - 44e^{3} + \frac{491}{17}e$ |
41 | $[41, 41, w^{2} + w - 11]$ | $\phantom{-}\frac{1}{51}e^{8} + \frac{3}{17}e^{6} - \frac{316}{51}e^{4} + 24e^{2} - \frac{378}{17}$ |
47 | $[47, 47, w^{2} + 2w - 1]$ | $-\frac{43}{51}e^{8} + \frac{752}{51}e^{6} - \frac{1245}{17}e^{4} + 127e^{2} - \frac{984}{17}$ |
59 | $[59, 59, w^{2} + w - 1]$ | $\phantom{-}\frac{19}{51}e^{8} - \frac{113}{17}e^{6} + \frac{1748}{51}e^{4} - 63e^{2} + \frac{468}{17}$ |
61 | $[61, 61, -w^{2} + 5w - 7]$ | $\phantom{-}\frac{15}{17}e^{8} - \frac{256}{17}e^{6} + \frac{1210}{17}e^{4} - 115e^{2} + \frac{874}{17}$ |
67 | $[67, 67, 2w^{2} - 13]$ | $\phantom{-}\frac{15}{17}e^{9} - \frac{273}{17}e^{7} + \frac{1465}{17}e^{5} - 166e^{3} + \frac{1418}{17}e$ |
89 | $[89, 89, -2w^{2} + w + 20]$ | $-\frac{11}{51}e^{8} + \frac{69}{17}e^{6} - \frac{1216}{51}e^{4} + 58e^{2} - \frac{738}{17}$ |
89 | $[89, 89, 5w^{2} + 8w - 19]$ | $-\frac{7}{51}e^{9} + \frac{124}{51}e^{7} - \frac{610}{51}e^{5} + 17e^{3} + \frac{11}{17}e$ |
89 | $[89, 89, w^{2} + 2w - 7]$ | $-\frac{22}{51}e^{9} + \frac{397}{51}e^{7} - \frac{2092}{51}e^{5} + 76e^{3} - \frac{592}{17}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, w + 2]$ | $1$ |