Base field 4.4.16400.1
Generator \(w\), with minimal polynomial \(x^{4} - 13x^{2} + 41\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11,11,-2w^{2} + w + 12]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 3x^{5} - 6x^{4} - 24x^{3} - 11x^{2} + 15x + 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{3} + 2w^{2} + 6w - 11]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w - 2]$ | $-e^{5} - 2e^{4} + 8e^{3} + 16e^{2} - 5e - 11$ |
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}\frac{2}{3}e^{5} + e^{4} - 5e^{3} - 8e^{2} + \frac{5}{3}e + 5$ |
| 11 | $[11, 11, -2w^{2} - w + 12]$ | $\phantom{-}\frac{2}{3}e^{5} + e^{4} - 5e^{3} - 8e^{2} + \frac{8}{3}e + 6$ |
| 11 | $[11, 11, 2w^{2} - w - 12]$ | $-1$ |
| 19 | $[19, 19, -w^{2} - w + 4]$ | $-\frac{2}{3}e^{5} - 2e^{4} + 5e^{3} + 16e^{2} - \frac{2}{3}e - 9$ |
| 19 | $[19, 19, w^{2} - w - 4]$ | $\phantom{-}\frac{4}{3}e^{5} + 2e^{4} - 11e^{3} - 15e^{2} + \frac{25}{3}e + 7$ |
| 29 | $[29, 29, -w - 1]$ | $-\frac{5}{3}e^{5} - 4e^{4} + 13e^{3} + 32e^{2} - \frac{20}{3}e - 23$ |
| 29 | $[29, 29, w - 1]$ | $-\frac{1}{3}e^{5} - e^{4} + 2e^{3} + 8e^{2} + \frac{14}{3}e - 3$ |
| 31 | $[31, 31, -2w^{2} - w + 14]$ | $-\frac{5}{3}e^{5} - 4e^{4} + 12e^{3} + 32e^{2} + \frac{1}{3}e - 17$ |
| 31 | $[31, 31, w^{3} - 3w^{2} - 6w + 19]$ | $-\frac{10}{3}e^{5} - 5e^{4} + 27e^{3} + 40e^{2} - \frac{61}{3}e - 22$ |
| 31 | $[31, 31, -w^{3} - 3w^{2} + 6w + 19]$ | $-\frac{4}{3}e^{5} - 3e^{4} + 11e^{3} + 25e^{2} - \frac{22}{3}e - 21$ |
| 31 | $[31, 31, -2w^{2} + w + 14]$ | $\phantom{-}e^{4} + e^{3} - 9e^{2} - 5e + 11$ |
| 41 | $[41, 41, -w]$ | $\phantom{-}\frac{1}{3}e^{5} + e^{4} - 3e^{3} - 9e^{2} + \frac{7}{3}e + 9$ |
| 71 | $[71, 71, w^{3} + 3w^{2} - 7w - 19]$ | $\phantom{-}e^{4} + 3e^{3} - 8e^{2} - 20e + 6$ |
| 71 | $[71, 71, w^{3} - 3w^{2} - 7w + 19]$ | $\phantom{-}4e^{5} + 6e^{4} - 33e^{3} - 49e^{2} + 24e + 31$ |
| 79 | $[79, 79, w^{3} + 3w^{2} - 9w - 25]$ | $\phantom{-}\frac{1}{3}e^{5} - 2e^{3} + \frac{4}{3}e - 1$ |
| 79 | $[79, 79, w^{3} - 3w^{2} - 9w + 25]$ | $-2e^{5} - 5e^{4} + 15e^{3} + 39e^{2} - 2e - 14$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{1}{3}e^{5} - 4e^{3} + \frac{43}{3}e - 3$ |
| 89 | $[89, 89, -w^{3} - 4w^{2} + 6w + 24]$ | $-\frac{13}{3}e^{5} - 9e^{4} + 34e^{3} + 69e^{2} - \frac{43}{3}e - 33$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11,11,-2w^{2} + w + 12]$ | $1$ |