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: | $[1, 1, 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 10x^{4} + 23x^{2} - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w^{3} + w^{2} + 5w - 2]$ | $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 9e$ |
| 11 | $[11, 11, -w^{3} + 5w + 1]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{11}{2}e^{3} + 13e$ |
| 11 | $[11, 11, -w + 2]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{2}e^{2} + 3$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 4w + 1]$ | $-e^{5} + 9e^{3} - 16e$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{11}{2}e^{3} + 15e$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $-\frac{1}{2}e^{4} + \frac{5}{2}e^{2} + 5$ |
| 23 | $[23, 23, w^{3} - 6w]$ | $\phantom{-}e^{4} - 7e^{2} + 6$ |
| 27 | $[27, 3, w^{3} + w^{2} - 5w - 4]$ | $-\frac{1}{2}e^{5} + \frac{13}{2}e^{3} - 19e$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 5w]$ | $\phantom{-}e^{5} - 11e^{3} + 32e$ |
| 41 | $[41, 41, 2w^{3} - 11w - 4]$ | $-\frac{1}{2}e^{5} + \frac{5}{2}e^{3} + e$ |
| 53 | $[53, 53, 2w^{3} - 2w^{2} - 11w + 6]$ | $\phantom{-}e^{5} - 9e^{3} + 18e$ |
| 59 | $[59, 59, 2w^{3} - 11w - 2]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{2} - 7$ |
| 67 | $[67, 67, w^{3} - 7w - 1]$ | $-\frac{3}{2}e^{4} + \frac{23}{2}e^{2} - 7$ |
| 71 | $[71, 71, 3w^{3} - 2w^{2} - 15w + 1]$ | $\phantom{-}2e^{5} - 20e^{3} + 42e$ |
| 79 | $[79, 79, -3w^{3} + w^{2} + 16w + 3]$ | $\phantom{-}e^{5} - 11e^{3} + 24e$ |
| 89 | $[89, 89, -4w^{3} + 2w^{2} + 22w - 3]$ | $\phantom{-}\frac{3}{2}e^{5} - \frac{25}{2}e^{3} + 21e$ |
| 101 | $[101, 101, -2w^{3} + 13w + 6]$ | $-4e^{2} + 14$ |
| 101 | $[101, 101, w^{3} + w^{2} - 6w - 3]$ | $-e^{4} + 7e^{2} - 4$ |
| 101 | $[101, 101, -3w^{3} + 2w^{2} + 17w - 3]$ | $-2e^{5} + 20e^{3} - 46e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).