Base field 4.4.19225.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 15x^{2} + 2x + 44\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 5x^{5} - x^{4} - 28x^{3} - 15x^{2} + 21x + 5\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{9}{2}w - 10]$ | $\phantom{-}e$ |
| 9 | $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - \frac{5}{2}w + 17]$ | $\phantom{-}\frac{1}{2}e^{5} + 2e^{4} - \frac{3}{2}e^{3} - \frac{19}{2}e^{2} - 2e + \frac{5}{2}$ |
| 9 | $[9, 3, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 28]$ | $\phantom{-}\frac{1}{2}e^{5} + 2e^{4} - \frac{3}{2}e^{3} - \frac{19}{2}e^{2} - 2e + \frac{5}{2}$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 11]$ | $-e^{3} - 2e^{2} + 5e + 4$ |
| 11 | $[11, 11, -w - 3]$ | $-e^{3} - 2e^{2} + 5e + 4$ |
| 25 | $[25, 5, w^{3} - 3w^{2} - 7w + 15]$ | $\phantom{-}e^{4} + 3e^{3} - 5e^{2} - 13e + 6$ |
| 29 | $[29, 29, w + 1]$ | $-\frac{1}{2}e^{5} - 2e^{4} + \frac{3}{2}e^{3} + \frac{21}{2}e^{2} + 5e - \frac{5}{2}$ |
| 29 | $[29, 29, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 9]$ | $-\frac{1}{2}e^{5} - 2e^{4} + \frac{3}{2}e^{3} + \frac{21}{2}e^{2} + 5e - \frac{5}{2}$ |
| 31 | $[31, 31, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 16]$ | $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 8e + 4$ |
| 31 | $[31, 31, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{9}{2}w + 5]$ | $-e^{3} - e^{2} + 5e - 1$ |
| 31 | $[31, 31, -w + 3]$ | $-e^{3} - e^{2} + 5e - 1$ |
| 31 | $[31, 31, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 29]$ | $\phantom{-}e^{4} + 2e^{3} - 7e^{2} - 8e + 4$ |
| 59 | $[59, 59, 2w^{2} - w - 13]$ | $-e^{4} - 2e^{3} + 5e^{2} + 4e$ |
| 59 | $[59, 59, \frac{9}{2}w^{3} - \frac{31}{2}w^{2} - \frac{61}{2}w + 85]$ | $-e^{4} - 2e^{3} + 5e^{2} + 4e$ |
| 61 | $[61, 61, 2w^{3} - 6w^{2} - 15w + 31]$ | $\phantom{-}\frac{1}{2}e^{5} + 2e^{4} - \frac{5}{2}e^{3} - \frac{21}{2}e^{2} + 6e + \frac{13}{2}$ |
| 61 | $[61, 61, -\frac{3}{2}w^{3} + \frac{11}{2}w^{2} + \frac{21}{2}w - 34]$ | $\phantom{-}\frac{1}{2}e^{5} + 2e^{4} - \frac{5}{2}e^{3} - \frac{21}{2}e^{2} + 6e + \frac{13}{2}$ |
| 71 | $[71, 71, \frac{3}{2}w^{3} - \frac{11}{2}w^{2} - \frac{19}{2}w + 32]$ | $-e^{4} - 3e^{3} + 3e^{2} + 9e + 4$ |
| 71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + \frac{5}{2}w - 13]$ | $-e^{4} - 3e^{3} + 3e^{2} + 9e + 4$ |
| 79 | $[79, 79, -3w^{3} + 10w^{2} + 19w - 51]$ | $-e^{5} - 4e^{4} + 3e^{3} + 22e^{2} + 10e - 10$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).