Base field 4.4.2525.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[71, 71, w^{3} + w^{2} - 4w - 6]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 3x^{3} - 18x^{2} + 44x + 40\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w]$ | $\phantom{-}2$ |
| 5 | $[5, 5, w^{3} - 2w^{2} - 2w + 3]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w^{2} + 4]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - \frac{9}{2}e - 2$ |
| 11 | $[11, 11, w^{2} - 2w - 3]$ | $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + \frac{7}{2}e + 6$ |
| 16 | $[16, 2, 2]$ | $-\frac{1}{4}e^{3} + \frac{1}{4}e^{2} + 3e - 2$ |
| 29 | $[29, 29, w^{3} - 4w - 1]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{1}{4}e^{2} - 3e + 3$ |
| 29 | $[29, 29, w^{3} - 3w^{2} - w + 4]$ | $-e$ |
| 41 | $[41, 41, w^{3} - 2w^{2} - w + 4]$ | $-e$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 2w + 2]$ | $-e$ |
| 59 | $[59, 59, -2w^{3} + 4w^{2} + 4w - 7]$ | $-e^{2} + 2e + 8$ |
| 59 | $[59, 59, -3w^{2} + 2w + 7]$ | $-\frac{3}{4}e^{3} - \frac{1}{4}e^{2} + 10e + 7$ |
| 61 | $[61, 61, -w^{3} + 4w^{2} - 6]$ | $-\frac{1}{4}e^{3} - \frac{3}{4}e^{2} + 3e + 9$ |
| 61 | $[61, 61, w^{3} + w^{2} - 5w - 3]$ | $\phantom{-}e^{2} + e - 8$ |
| 71 | $[71, 71, w^{3} + w^{2} - 4w - 6]$ | $-1$ |
| 71 | $[71, 71, 3w^{2} - 2w - 8]$ | $-\frac{3}{4}e^{3} - \frac{3}{4}e^{2} + \frac{23}{2}e + 12$ |
| 71 | $[71, 71, 3w^{2} - 4w - 7]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - 7e - 8$ |
| 71 | $[71, 71, w^{3} - 4w^{2} + w + 8]$ | $\phantom{-}e^{2} - 2e - 12$ |
| 79 | $[79, 79, -2w^{3} + 3w^{2} + 5w - 2]$ | $-e^{2} - e + 10$ |
| 79 | $[79, 79, 2w^{2} - 3w - 7]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{5}{4}e^{2} - 2e + 11$ |
| 79 | $[79, 79, 2w^{2} - w - 8]$ | $\phantom{-}\frac{3}{4}e^{3} - \frac{1}{4}e^{2} - \frac{25}{2}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $71$ | $[71, 71, w^{3} + w^{2} - 4w - 6]$ | $1$ |