Base field 4.4.19821.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} + 6x + 3\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[13, 13, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 5w]$ |
Dimension: | $21$ |
CM: | no |
Base change: | no |
Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{21} - 5x^{20} - 36x^{19} + 201x^{18} + 521x^{17} - 3385x^{16} - 3882x^{15} + 31152x^{14} + 16004x^{13} - 171537x^{12} - 38817x^{11} + 581682x^{10} + 75439x^{9} - 1200833x^{8} - 183813x^{7} + 1420731x^{6} + 357529x^{5} - 826350x^{4} - 322239x^{3} + 152928x^{2} + 90963x + 11421\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}e$ |
7 | $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 2w + 2]$ | $...$ |
9 | $[9, 3, w + 1]$ | $...$ |
13 | $[13, 13, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 5w]$ | $-1$ |
16 | $[16, 2, 2]$ | $...$ |
17 | $[17, 17, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 3w + 5]$ | $...$ |
19 | $[19, 19, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w - 5]$ | $...$ |
23 | $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 2]$ | $...$ |
25 | $[25, 5, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w]$ | $...$ |
25 | $[25, 5, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 3]$ | $...$ |
29 | $[29, 29, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 4w - 3]$ | $...$ |
29 | $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w]$ | $...$ |
37 | $[37, 37, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ | $...$ |
41 | $[41, 41, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 4]$ | $...$ |
43 | $[43, 43, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w]$ | $...$ |
47 | $[47, 47, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w]$ | $...$ |
59 | $[59, 59, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 4]$ | $...$ |
59 | $[59, 59, \frac{4}{3}w^{3} - \frac{5}{3}w^{2} - 10w + 9]$ | $...$ |
67 | $[67, 67, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w]$ | $...$ |
71 | $[71, 71, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 5w]$ | $1$ |