Base field 4.4.17989.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[5, 5, w^{3} - 2w^{2} - 6w + 2]$ |
| Dimension: | $5$ |
| 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:
| \(x^{5} - x^{4} - 12x^{3} + 5x^{2} + 36x + 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + 2w^{2} + 4w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{3} - 2w^{2} - 6w + 2]$ | $-1$ |
| 11 | $[11, 11, w^{3} - 2w^{2} - 4w]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + 5e^{2} + \frac{7}{2}e - 6$ |
| 13 | $[13, 13, w^{2} - 3w - 2]$ | $\phantom{-}e^{3} - 7e - 2$ |
| 16 | $[16, 2, 2]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + 2e^{2} + \frac{11}{2}e + 8$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ | $\phantom{-}e^{4} + e^{3} - 7e^{2} - 10e$ |
| 17 | $[17, 17, -w^{2} + 2w + 3]$ | $-e^{3} + 8e + 4$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 6w + 1]$ | $\phantom{-}e^{4} - 8e^{2} - 2e + 8$ |
| 27 | $[27, 3, -2w^{3} + 3w^{2} + 11w - 1]$ | $-\frac{1}{2}e^{4} - \frac{3}{2}e^{3} + 2e^{2} + \frac{27}{2}e + 14$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 5w + 4]$ | $\phantom{-}e^{3} - e^{2} - 5e + 3$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 6w - 3]$ | $-2e^{3} - e^{2} + 14e + 13$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 5w + 1]$ | $-e^{4} + 8e^{2} + e - 3$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 6w]$ | $\phantom{-}2e^{3} + e^{2} - 14e - 10$ |
| 31 | $[31, 31, -w^{2} + 2w + 1]$ | $-\frac{1}{2}e^{4} - \frac{3}{2}e^{3} + 4e^{2} + \frac{25}{2}e$ |
| 37 | $[37, 37, w^{3} - w^{2} - 7w - 1]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - 5e^{2} + \frac{9}{2}e + 10$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $\phantom{-}2e^{3} - e^{2} - 13e + 2$ |
| 71 | $[71, 71, w^{3} - 2w^{2} - 6w - 1]$ | $-2e^{3} - e^{2} + 13e + 6$ |
| 71 | $[71, 71, 5w^{3} - 8w^{2} - 29w + 3]$ | $\phantom{-}2e^{3} + 2e^{2} - 18e - 12$ |
| 89 | $[89, 89, -2w^{3} + 4w^{2} + 10w - 7]$ | $-\frac{3}{2}e^{4} + \frac{1}{2}e^{3} + 11e^{2} - \frac{5}{2}e - 10$ |
| 97 | $[97, 97, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - 5e^{2} - \frac{13}{2}e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w^{3} - 2w^{2} - 6w + 2]$ | $1$ |