Base field 4.4.7625.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 9x^{2} + 4x + 16\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[29, 29, \frac{1}{4}w^{3} - \frac{1}{4}w^{2} - \frac{1}{4}w + 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 4x^{5} - 5x^{4} + 35x^{3} - 19x^{2} - 55x + 51\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{3}{2}w + 4]$ | $\phantom{-}e$ |
| 4 | $[4, 2, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 5]$ | $\phantom{-}\frac{3}{2}e^{5} - \frac{7}{2}e^{4} - 13e^{3} + \frac{61}{2}e^{2} + 20e - \frac{93}{2}$ |
| 5 | $[5, 5, -\frac{1}{4}w^{3} - \frac{3}{4}w^{2} + \frac{5}{4}w + 3]$ | $-e^{5} + 2e^{4} + 9e^{3} - 17e^{2} - 15e + 25$ |
| 11 | $[11, 11, -\frac{1}{4}w^{3} + \frac{1}{4}w^{2} + \frac{9}{4}w]$ | $-e^{5} + 3e^{4} + 9e^{3} - 27e^{2} - 14e + 44$ |
| 11 | $[11, 11, w - 1]$ | $\phantom{-}4e^{5} - 8e^{4} - 35e^{3} + 70e^{2} + 55e - 109$ |
| 29 | $[29, 29, \frac{1}{4}w^{3} - \frac{1}{4}w^{2} - \frac{1}{4}w + 2]$ | $-1$ |
| 29 | $[29, 29, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + 3]$ | $-e^{5} + 2e^{4} + 8e^{3} - 17e^{2} - 10e + 30$ |
| 31 | $[31, 31, -\frac{3}{4}w^{3} - \frac{1}{4}w^{2} + \frac{19}{4}w + 4]$ | $-e^{5} - e^{4} + 9e^{3} + 9e^{2} - 17e - 15$ |
| 31 | $[31, 31, -\frac{3}{4}w^{3} + \frac{7}{4}w^{2} + \frac{11}{4}w - 5]$ | $-e^{5} + 2e^{4} + 8e^{3} - 16e^{2} - 8e + 21$ |
| 49 | $[49, 7, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 5]$ | $-2e^{5} + 5e^{4} + 18e^{3} - 42e^{2} - 31e + 63$ |
| 49 | $[49, 7, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ | $\phantom{-}3e^{5} - 4e^{4} - 27e^{3} + 37e^{2} + 45e - 60$ |
| 59 | $[59, 59, -\frac{1}{4}w^{3} + \frac{5}{4}w^{2} + \frac{5}{4}w - 3]$ | $\phantom{-}4e^{5} - 6e^{4} - 33e^{3} + 51e^{2} + 46e - 75$ |
| 59 | $[59, 59, w^{2} - 7]$ | $-5e^{5} + 6e^{4} + 43e^{3} - 53e^{2} - 66e + 84$ |
| 61 | $[61, 61, -\frac{5}{4}w^{3} - \frac{7}{4}w^{2} + \frac{37}{4}w + 15]$ | $-e^{4} - e^{3} + 8e^{2} + 4e - 7$ |
| 71 | $[71, 71, \frac{3}{4}w^{3} + \frac{9}{4}w^{2} - \frac{11}{4}w - 7]$ | $-3e^{5} + 5e^{4} + 27e^{3} - 47e^{2} - 45e + 80$ |
| 71 | $[71, 71, \frac{1}{4}w^{3} - \frac{1}{4}w^{2} - \frac{13}{4}w - 2]$ | $-5e^{5} + 9e^{4} + 45e^{3} - 78e^{2} - 74e + 119$ |
| 79 | $[79, 79, -\frac{1}{4}w^{3} + \frac{5}{4}w^{2} + \frac{1}{4}w - 7]$ | $-4e^{5} + 7e^{4} + 36e^{3} - 63e^{2} - 61e + 105$ |
| 79 | $[79, 79, \frac{1}{4}w^{3} + \frac{3}{4}w^{2} - \frac{9}{4}w - 2]$ | $\phantom{-}4e^{5} - 9e^{4} - 35e^{3} + 79e^{2} + 56e - 120$ |
| 81 | $[81, 3, -3]$ | $-e^{5} + 6e^{4} + 9e^{3} - 53e^{2} - 14e + 84$ |
| 89 | $[89, 89, -w^{2} + 2w + 1]$ | $-4e^{4} + 2e^{3} + 33e^{2} - 11e - 48$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, \frac{1}{4}w^{3} - \frac{1}{4}w^{2} - \frac{1}{4}w + 2]$ | $1$ |