Base field 4.4.19429.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[5, 5, w]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 3x^{5} - 6x^{4} - 21x^{3} - 4x^{2} + 13x + 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $-1$ |
| 7 | $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ | $\phantom{-}\frac{1}{2}e^{4} + e^{3} - \frac{7}{2}e^{2} - 5e + \frac{3}{2}$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $-\frac{1}{2}e^{5} - \frac{3}{2}e^{4} + \frac{7}{2}e^{3} + \frac{19}{2}e^{2} - \frac{5}{2}e - \frac{7}{2}$ |
| 13 | $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ | $-\frac{1}{2}e^{5} - \frac{1}{2}e^{4} + \frac{9}{2}e^{3} + \frac{5}{2}e^{2} - \frac{15}{2}e + \frac{3}{2}$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}e^{3} - 6e$ |
| 17 | $[17, 17, -w + 2]$ | $\phantom{-}e^{5} + 2e^{4} - 7e^{3} - 12e^{2} + 3e + 2$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}e^{5} + 2e^{4} - 7e^{3} - 12e^{2} + 3e + 2$ |
| 27 | $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ | $\phantom{-}\frac{1}{2}e^{5} + \frac{3}{2}e^{4} - \frac{7}{2}e^{3} - \frac{23}{2}e^{2} + \frac{1}{2}e + \frac{19}{2}$ |
| 31 | $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ | $\phantom{-}\frac{3}{2}e^{5} + 3e^{4} - \frac{23}{2}e^{3} - 20e^{2} + \frac{25}{2}e + 13$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 6w + 1]$ | $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 2e^{2} - \frac{13}{2}e + 5$ |
| 41 | $[41, 41, w^{2} - w - 1]$ | $\phantom{-}\frac{3}{2}e^{5} + 3e^{4} - \frac{23}{2}e^{3} - 21e^{2} + \frac{21}{2}e + 12$ |
| 43 | $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ | $\phantom{-}\frac{1}{2}e^{5} + e^{4} - \frac{5}{2}e^{3} - 6e^{2} - \frac{9}{2}e + 3$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ | $\phantom{-}e^{5} + 2e^{4} - 7e^{3} - 14e^{2} + e + 10$ |
| 53 | $[53, 53, -w - 3]$ | $-e^{5} - \frac{5}{2}e^{4} + 7e^{3} + \frac{33}{2}e^{2} - 3e - \frac{7}{2}$ |
| 53 | $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ | $\phantom{-}e^{5} + 2e^{4} - 7e^{3} - 14e^{2} + e + 4$ |
| 59 | $[59, 59, 2w^{2} - 3w - 6]$ | $-e^{5} - e^{4} + 10e^{3} + 7e^{2} - 20e - 5$ |
| 59 | $[59, 59, w^{3} - w^{2} - 7w - 3]$ | $-\frac{3}{2}e^{5} - \frac{7}{2}e^{4} + \frac{25}{2}e^{3} + \frac{51}{2}e^{2} - \frac{35}{2}e - \frac{39}{2}$ |
| 79 | $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ | $\phantom{-}\frac{1}{2}e^{5} + \frac{1}{2}e^{4} - \frac{11}{2}e^{3} - \frac{3}{2}e^{2} + \frac{33}{2}e + \frac{1}{2}$ |
| 79 | $[79, 79, w^{2} - 2w - 1]$ | $-2e^{5} - 5e^{4} + 14e^{3} + 31e^{2} - 6e - 7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w]$ | $1$ |