Base field 4.4.15952.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 2x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, -w^{3} + w^{2} + 4w + 1]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 3x^{13} - 16x^{12} + 52x^{11} + 88x^{10} - 332x^{9} - 189x^{8} + 990x^{7} + 65x^{6} - 1421x^{5} + 281x^{4} + 867x^{3} - 285x^{2} - 129x + 34\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w^{3} + w^{2} + 5w - 2]$ | $...$ |
| 11 | $[11, 11, -w^{3} + 5w + 1]$ | $...$ |
| 11 | $[11, 11, -w + 2]$ | $...$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 4w + 1]$ | $-1$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ | $...$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $...$ |
| 23 | $[23, 23, w^{3} - 6w]$ | $...$ |
| 27 | $[27, 3, w^{3} + w^{2} - 5w - 4]$ | $...$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 5w]$ | $...$ |
| 41 | $[41, 41, 2w^{3} - 11w - 4]$ | $...$ |
| 53 | $[53, 53, 2w^{3} - 2w^{2} - 11w + 6]$ | $...$ |
| 59 | $[59, 59, 2w^{3} - 11w - 2]$ | $...$ |
| 67 | $[67, 67, w^{3} - 7w - 1]$ | $...$ |
| 71 | $[71, 71, 3w^{3} - 2w^{2} - 15w + 1]$ | $...$ |
| 79 | $[79, 79, -3w^{3} + w^{2} + 16w + 3]$ | $...$ |
| 89 | $[89, 89, -4w^{3} + 2w^{2} + 22w - 3]$ | $...$ |
| 101 | $[101, 101, -2w^{3} + 13w + 6]$ | $...$ |
| 101 | $[101, 101, w^{3} + w^{2} - 6w - 3]$ | $...$ |
| 101 | $[101, 101, -3w^{3} + 2w^{2} + 17w - 3]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -w^{3} + w^{2} + 4w + 1]$ | $1$ |