Base field 3.3.1345.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[5, 5, w + 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 7x^{3} + 5x^{2} - 39x - 45\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $-1$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}\frac{2}{3}e^{3} + \frac{5}{3}e^{2} - \frac{17}{3}e - 6$ |
| 7 | $[7, 7, -w + 2]$ | $-\frac{1}{3}e^{3} - \frac{4}{3}e^{2} + \frac{7}{3}e + 6$ |
| 7 | $[7, 7, -w + 1]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{4}{3}e^{2} - \frac{7}{3}e - 7$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}e^{3} + 3e^{2} - 7e - 12$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $-\frac{2}{3}e^{3} - \frac{5}{3}e^{2} + \frac{17}{3}e + 5$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $-\frac{1}{3}e^{3} - \frac{1}{3}e^{2} + \frac{10}{3}e - 3$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $-e^{3} - 3e^{2} + 6e + 9$ |
| 27 | $[27, 3, 3]$ | $-e^{3} - 3e^{2} + 6e + 10$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $-e^{3} - 4e^{2} + 6e + 18$ |
| 31 | $[31, 31, w^{2} - w - 8]$ | $\phantom{-}\frac{4}{3}e^{3} + \frac{10}{3}e^{2} - \frac{34}{3}e - 13$ |
| 37 | $[37, 37, -w - 4]$ | $-\frac{5}{3}e^{3} - \frac{17}{3}e^{2} + \frac{29}{3}e + 26$ |
| 43 | $[43, 43, 2w^{2} - 4w - 3]$ | $-\frac{4}{3}e^{3} - \frac{16}{3}e^{2} + \frac{22}{3}e + 21$ |
| 47 | $[47, 47, w^{2} - 3]$ | $\phantom{-}e^{3} + 4e^{2} - 5e - 12$ |
| 53 | $[53, 53, 2w^{2} - w - 11]$ | $-e^{3} - 3e^{2} + 7e + 9$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $-e^{3} - 2e^{2} + 8e$ |
| 67 | $[67, 67, w^{2} + w - 8]$ | $-e^{3} - 3e^{2} + 9e + 14$ |
| 71 | $[71, 71, w^{2} + w - 11]$ | $-2e^{3} - 7e^{2} + 11e + 21$ |
| 73 | $[73, 73, -w^{2} + 4w - 2]$ | $\phantom{-}\frac{11}{3}e^{3} + \frac{38}{3}e^{2} - \frac{62}{3}e - 45$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w + 2]$ | $1$ |