Base field 4.4.9792.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 2x + 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 4x^{3} - 28x^{2} + 64x + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{3} - 3w^{2} - 3w + 4]$ | $\phantom{-}\frac{1}{14}e^{3} - \frac{3}{14}e^{2} - \frac{12}{7}e + \frac{20}{7}$ |
| 7 | $[7, 7, w]$ | $-\frac{1}{14}e^{3} + \frac{3}{14}e^{2} + \frac{12}{7}e - \frac{6}{7}$ |
| 7 | $[7, 7, w^{3} - 3w^{2} - 4w + 5]$ | $-\frac{1}{14}e^{3} + \frac{3}{14}e^{2} + \frac{12}{7}e - \frac{6}{7}$ |
| 9 | $[9, 3, w^{3} - 4w^{2} - w + 9]$ | $\phantom{-}\frac{1}{14}e^{3} - \frac{3}{14}e^{2} - \frac{19}{7}e + \frac{20}{7}$ |
| 17 | $[17, 17, 2w^{3} - 6w^{2} - 7w + 8]$ | $-\frac{1}{2}e^{2} + e + 8$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} + 4w - 3]$ | $\phantom{-}\frac{1}{28}e^{3} + \frac{1}{7}e^{2} - \frac{13}{7}e - \frac{18}{7}$ |
| 17 | $[17, 17, -w + 2]$ | $\phantom{-}\frac{1}{28}e^{3} + \frac{1}{7}e^{2} - \frac{13}{7}e - \frac{18}{7}$ |
| 23 | $[23, 23, 2w^{3} - 7w^{2} - 4w + 12]$ | $-\frac{1}{7}e^{3} + \frac{3}{7}e^{2} + \frac{38}{7}e - \frac{40}{7}$ |
| 23 | $[23, 23, -w^{2} + 2w + 3]$ | $-\frac{1}{7}e^{3} + \frac{3}{7}e^{2} + \frac{38}{7}e - \frac{40}{7}$ |
| 31 | $[31, 31, -2w^{3} + 7w^{2} + 5w - 12]$ | $\phantom{-}\frac{1}{14}e^{3} - \frac{3}{14}e^{2} - \frac{12}{7}e - \frac{22}{7}$ |
| 31 | $[31, 31, -w^{3} + 4w^{2} + 2w - 8]$ | $\phantom{-}\frac{1}{14}e^{3} - \frac{3}{14}e^{2} - \frac{12}{7}e - \frac{22}{7}$ |
| 41 | $[41, 41, 3w^{3} - 10w^{2} - 7w + 16]$ | $-\frac{3}{28}e^{3} + \frac{4}{7}e^{2} + \frac{25}{7}e - \frac{58}{7}$ |
| 41 | $[41, 41, 2w^{3} - 7w^{2} - 5w + 10]$ | $-\frac{3}{28}e^{3} + \frac{4}{7}e^{2} + \frac{25}{7}e - \frac{58}{7}$ |
| 49 | $[49, 7, 2w^{3} - 6w^{2} - 6w + 9]$ | $\phantom{-}\frac{3}{14}e^{3} - \frac{9}{14}e^{2} - \frac{36}{7}e + \frac{74}{7}$ |
| 71 | $[71, 71, w^{2} - 2w - 2]$ | $\phantom{-}\frac{1}{14}e^{3} - \frac{5}{7}e^{2} - \frac{12}{7}e + \frac{76}{7}$ |
| 71 | $[71, 71, 2w^{3} - 7w^{2} - 4w + 13]$ | $\phantom{-}\frac{1}{14}e^{3} - \frac{5}{7}e^{2} - \frac{12}{7}e + \frac{76}{7}$ |
| 73 | $[73, 73, 3w^{3} - 11w^{2} - 5w + 19]$ | $-\frac{1}{14}e^{3} + \frac{3}{14}e^{2} + \frac{12}{7}e - \frac{6}{7}$ |
| 73 | $[73, 73, -4w^{3} + 13w^{2} + 10w - 17]$ | $-\frac{1}{14}e^{3} + \frac{3}{14}e^{2} + \frac{12}{7}e - \frac{6}{7}$ |
| 79 | $[79, 79, 3w^{3} - 9w^{2} - 10w + 13]$ | $-\frac{5}{14}e^{3} + \frac{15}{14}e^{2} + \frac{60}{7}e - \frac{58}{7}$ |
| 79 | $[79, 79, -2w^{3} + 6w^{2} + 5w - 8]$ | $-\frac{5}{14}e^{3} + \frac{15}{14}e^{2} + \frac{60}{7}e - \frac{58}{7}$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).