Base field 4.4.14336.1
Generator \(w\), with minimal polynomial \(x^{4} - 8x^{2} + 14\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[14, 14, -w^{2} - w + 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 5x^{3} - 8x^{2} + 45x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{3} + w^{2} + 5w - 6]$ | $-1$ |
| 7 | $[7, 7, w^{3} - w^{2} - 5w + 7]$ | $\phantom{-}\frac{2}{7}e^{3} - \frac{5}{7}e^{2} - \frac{18}{7}e + \frac{24}{7}$ |
| 7 | $[7, 7, -w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 1]$ | $-1$ |
| 17 | $[17, 17, w^{2} - w - 5]$ | $\phantom{-}\frac{2}{7}e^{3} - \frac{5}{7}e^{2} - \frac{25}{7}e + \frac{31}{7}$ |
| 17 | $[17, 17, w^{2} + w - 5]$ | $\phantom{-}2e - 2$ |
| 23 | $[23, 23, -w - 3]$ | $-\frac{1}{7}e^{3} - \frac{1}{7}e^{2} + \frac{16}{7}e + \frac{23}{7}$ |
| 23 | $[23, 23, w - 3]$ | $\phantom{-}\frac{4}{7}e^{3} - \frac{10}{7}e^{2} - \frac{43}{7}e + \frac{48}{7}$ |
| 25 | $[25, 5, -w^{3} + w^{2} + 4w - 3]$ | $\phantom{-}e - 4$ |
| 25 | $[25, 5, -w^{3} - w^{2} + 4w + 3]$ | $\phantom{-}\frac{1}{7}e^{3} - \frac{6}{7}e^{2} - \frac{9}{7}e + \frac{26}{7}$ |
| 41 | $[41, 41, w^{3} - 4w - 1]$ | $\phantom{-}e^{2} - 2e - 10$ |
| 41 | $[41, 41, -w^{3} + 4w - 1]$ | $-\frac{1}{7}e^{3} - \frac{1}{7}e^{2} + \frac{2}{7}e + \frac{37}{7}$ |
| 71 | $[71, 71, -w^{3} + 2w^{2} + 4w - 9]$ | $-\frac{1}{7}e^{3} - \frac{1}{7}e^{2} + \frac{16}{7}e + \frac{37}{7}$ |
| 71 | $[71, 71, w^{3} + 2w^{2} - 4w - 9]$ | $-\frac{4}{7}e^{3} + \frac{3}{7}e^{2} + \frac{50}{7}e + \frac{22}{7}$ |
| 73 | $[73, 73, w^{3} - w^{2} - 5w + 3]$ | $-\frac{1}{7}e^{3} - \frac{1}{7}e^{2} + \frac{2}{7}e + \frac{65}{7}$ |
| 73 | $[73, 73, w^{3} + w^{2} - 5w - 3]$ | $-\frac{1}{7}e^{3} - \frac{8}{7}e^{2} + \frac{37}{7}e + \frac{58}{7}$ |
| 79 | $[79, 79, 2w^{2} - 2w - 9]$ | $\phantom{-}\frac{2}{7}e^{3} + \frac{2}{7}e^{2} - \frac{18}{7}e - \frac{60}{7}$ |
| 79 | $[79, 79, -2w^{3} + 8w + 5]$ | $-\frac{1}{7}e^{3} + \frac{6}{7}e^{2} + \frac{2}{7}e + \frac{9}{7}$ |
| 81 | $[81, 3, -3]$ | $-\frac{2}{7}e^{3} - \frac{2}{7}e^{2} + \frac{46}{7}e + \frac{4}{7}$ |
| 89 | $[89, 89, -w^{3} - 2w^{2} + 6w + 13]$ | $\phantom{-}\frac{1}{7}e^{3} + \frac{8}{7}e^{2} - \frac{37}{7}e - \frac{86}{7}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w^{3}+w^{2}+5w-6]$ | $1$ |
| $7$ | $[7,7,w-1]$ | $1$ |