Base field 4.4.19796.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 8\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ |
| Dimension: | $23$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $46$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{23} + x^{22} - 33x^{21} - 31x^{20} + 466x^{19} + 411x^{18} - 3687x^{17} - 3057x^{16} + 17971x^{15} + 14042x^{14} - 55880x^{13} - 41217x^{12} + 110998x^{11} + 76994x^{10} - 137190x^{9} - 87680x^{8} + 99858x^{7} + 54906x^{6} - 39760x^{5} - 15060x^{4} + 8571x^{3} + 1159x^{2} - 780x + 71\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + 2]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ | $...$ |
| 5 | $[5, 5, -w^{3} + 2w^{2} + 3w - 1]$ | $...$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ | $-1$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $...$ |
| 19 | $[19, 19, -w^{3} + 3w^{2} + 2w - 7]$ | $...$ |
| 23 | $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ | $...$ |
| 31 | $[31, 31, -w^{2} + w + 1]$ | $...$ |
| 47 | $[47, 47, -w^{3} + w^{2} + 4w - 3]$ | $...$ |
| 49 | $[49, 7, 2w^{3} - 5w^{2} - 7w + 11]$ | $...$ |
| 53 | $[53, 53, -3w^{3} + 9w^{2} + 10w - 31]$ | $...$ |
| 53 | $[53, 53, w^{3} - w^{2} - 4w + 1]$ | $...$ |
| 61 | $[61, 61, 3w^{3} - 6w^{2} - 13w + 13]$ | $...$ |
| 61 | $[61, 61, 2w^{2} - 7]$ | $...$ |
| 71 | $[71, 71, w^{2} - 3w - 5]$ | $...$ |
| 73 | $[73, 73, 2w - 3]$ | $...$ |
| 73 | $[73, 73, -2w^{3} + 6w^{2} + 6w - 19]$ | $...$ |
| 79 | $[79, 79, 2w^{2} - 5]$ | $...$ |
| 81 | $[81, 3, -3]$ | $...$ |
| 101 | $[101, 101, 2w^{2} - 4w - 9]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ | $1$ |