Base field 4.4.19821.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} + 6x + 3\); narrow class number \(1\) 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:
| \(x^{6} - 12x^{4} - x^{3} + 33x^{2} - 6x - 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 2w + 2]$ | $-e^{4} + 2e^{3} + 7e^{2} - 10e - 2$ |
| 9 | $[9, 3, w + 1]$ | $\phantom{-}\frac{1}{2}e^{5} - e^{4} - 4e^{3} + \frac{11}{2}e^{2} + \frac{11}{2}e - 1$ |
| 13 | $[13, 13, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 5w]$ | $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} - \frac{1}{2}e^{2} + \frac{15}{2}e - 2$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}e^{4} - e^{3} - 8e^{2} + 3e + 7$ |
| 17 | $[17, 17, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 3w + 5]$ | $-\frac{1}{2}e^{5} + e^{4} + 3e^{3} - \frac{11}{2}e^{2} + \frac{1}{2}e + 3$ |
| 19 | $[19, 19, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w - 5]$ | $\phantom{-}e^{4} - e^{3} - 8e^{2} + 3e + 10$ |
| 23 | $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 2]$ | $-e^{5} + 9e^{3} + 4e^{2} - 12e - 6$ |
| 25 | $[25, 5, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w]$ | $-\frac{1}{2}e^{5} + 5e^{3} + \frac{3}{2}e^{2} - \frac{19}{2}e + 1$ |
| 25 | $[25, 5, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 3]$ | $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} - \frac{5}{2}e^{2} + \frac{17}{2}e + 5$ |
| 29 | $[29, 29, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 4w - 3]$ | $-\frac{1}{2}e^{5} + e^{4} + 3e^{3} - \frac{11}{2}e^{2} + \frac{7}{2}e + 3$ |
| 29 | $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w]$ | $\phantom{-}\frac{1}{2}e^{5} - 2e^{4} - 3e^{3} + \frac{29}{2}e^{2} + \frac{1}{2}e - 12$ |
| 37 | $[37, 37, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ | $-\frac{1}{2}e^{5} + e^{4} + 4e^{3} - \frac{9}{2}e^{2} - \frac{9}{2}e - 4$ |
| 41 | $[41, 41, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 4]$ | $\phantom{-}\frac{1}{2}e^{5} - 6e^{3} - \frac{1}{2}e^{2} + \frac{27}{2}e$ |
| 43 | $[43, 43, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w]$ | $-e^{4} + e^{3} + 7e^{2} - e - 4$ |
| 47 | $[47, 47, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w]$ | $-e^{5} + 2e^{4} + 6e^{3} - 11e^{2} + 4e + 6$ |
| 59 | $[59, 59, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 4]$ | $\phantom{-}3e^{4} - 3e^{3} - 24e^{2} + 12e + 18$ |
| 59 | $[59, 59, \frac{4}{3}w^{3} - \frac{5}{3}w^{2} - 10w + 9]$ | $-e^{5} + e^{4} + 9e^{3} - 5e^{2} - 16e$ |
| 67 | $[67, 67, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w]$ | $\phantom{-}e^{3} - 2e^{2} - 8e + 2$ |
| 71 | $[71, 71, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ | $-e^{5} - e^{4} + 12e^{3} + 10e^{2} - 26e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).