Base field 4.4.17989.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, w^{2} - 3w - 2]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - x^{11} - 24x^{10} + 13x^{9} + 212x^{8} - 17x^{7} - 805x^{6} - 267x^{5} + 1083x^{4} + 663x^{3} - 115x^{2} - 76x + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + 2w^{2} + 4w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{3} - 2w^{2} - 6w + 2]$ | $...$ |
| 11 | $[11, 11, w^{3} - 2w^{2} - 4w]$ | $...$ |
| 13 | $[13, 13, w^{2} - 3w - 2]$ | $-1$ |
| 16 | $[16, 2, 2]$ | $...$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ | $...$ |
| 17 | $[17, 17, -w^{2} + 2w + 3]$ | $...$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 6w + 1]$ | $...$ |
| 27 | $[27, 3, -2w^{3} + 3w^{2} + 11w - 1]$ | $...$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 5w + 4]$ | $...$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 6w - 3]$ | $...$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 5w + 1]$ | $...$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 6w]$ | $...$ |
| 31 | $[31, 31, -w^{2} + 2w + 1]$ | $...$ |
| 37 | $[37, 37, w^{3} - w^{2} - 7w - 1]$ | $...$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $...$ |
| 71 | $[71, 71, w^{3} - 2w^{2} - 6w - 1]$ | $...$ |
| 71 | $[71, 71, 5w^{3} - 8w^{2} - 29w + 3]$ | $-\frac{265}{926}e^{11} + \frac{419}{926}e^{10} + \frac{3060}{463}e^{9} - \frac{7019}{926}e^{8} - \frac{26061}{463}e^{7} + \frac{34959}{926}e^{6} + \frac{193135}{926}e^{5} - \frac{41447}{926}e^{4} - \frac{263723}{926}e^{3} - \frac{25589}{926}e^{2} + \frac{41079}{926}e - \frac{1349}{463}$ |
| 89 | $[89, 89, -2w^{3} + 4w^{2} + 10w - 7]$ | $...$ |
| 97 | $[97, 97, -w^{3} + 2w^{2} + 4w - 4]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w^{2} - 3w - 2]$ | $1$ |