Base field 4.4.17609.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 10x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11, 11, -w^{3} + 6w - 4]$ |
| Dimension: | $13$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{13} + 4x^{12} - 11x^{11} - 56x^{10} + 31x^{9} + 282x^{8} + 27x^{7} - 622x^{6} - 214x^{5} + 579x^{4} + 250x^{3} - 175x^{2} - 81x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{3} + w^{2} - 4w + 1]$ | $...$ |
| 7 | $[7, 7, -w^{3} + 6w - 2]$ | $...$ |
| 8 | $[8, 2, w^{3} - 7w + 3]$ | $...$ |
| 11 | $[11, 11, -w^{3} + 6w - 4]$ | $\phantom{-}1$ |
| 17 | $[17, 17, w^{3} + w^{2} - 6w - 1]$ | $...$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $...$ |
| 31 | $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ | $...$ |
| 37 | $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ | $...$ |
| 41 | $[41, 41, w^{2} + 2w - 4]$ | $...$ |
| 47 | $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ | $...$ |
| 47 | $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ | $...$ |
| 59 | $[59, 59, -2w^{3} + 13w - 6]$ | $...$ |
| 59 | $[59, 59, -w^{3} - w^{2} + 5w + 2]$ | $...$ |
| 59 | $[59, 59, w^{2} + w - 1]$ | $-\frac{48}{293}e^{12} - \frac{87}{293}e^{11} + \frac{700}{293}e^{10} + \frac{1230}{293}e^{9} - \frac{3556}{293}e^{8} - \frac{6563}{293}e^{7} + \frac{6816}{293}e^{6} + \frac{16704}{293}e^{5} - \frac{777}{293}e^{4} - \frac{19628}{293}e^{3} - \frac{9571}{293}e^{2} + \frac{7270}{293}e + \frac{3990}{293}$ |
| 59 | $[59, 59, w^{2} + 2w - 6]$ | $...$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 8w - 7]$ | $...$ |
| 67 | $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ | $...$ |
| 73 | $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ | $...$ |
| 81 | $[81, 3, -3]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -w^{3} + 6w - 4]$ | $-1$ |