Base field 6.6.434581.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 4x^{4} + 5x^{3} + 4x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[71,71,-w^{5} + 4w^{4} - 11w^{2} + 2w + 4]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 4x^{2} - 24x + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 13 | $[13, 13, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + w + 4]$ | $-e + 2$ |
| 13 | $[13, 13, -w^{2} + w + 2]$ | $\phantom{-}e$ |
| 27 | $[27, 3, 2w^{5} - 4w^{4} - 7w^{3} + 9w^{2} + 4w - 2]$ | $\phantom{-}\frac{1}{4}e^{2} - \frac{3}{2}e - 5$ |
| 27 | $[27, 3, -2w^{5} + 5w^{4} + 5w^{3} - 12w^{2} - w + 5]$ | $\phantom{-}2$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 2w + 3]$ | $-\frac{1}{4}e^{2} + 5$ |
| 29 | $[29, 29, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 4w - 2]$ | $\phantom{-}\frac{1}{4}e^{2} - e$ |
| 43 | $[43, 43, -w^{5} + 3w^{4} + w^{3} - 6w^{2} + 3w + 1]$ | $-\frac{1}{2}e^{2} + \frac{7}{2}e + 11$ |
| 43 | $[43, 43, -w^{4} + w^{3} + 5w^{2} - 4]$ | $-\frac{1}{2}e^{2} + e + 8$ |
| 49 | $[49, 7, w^{5} - 4w^{4} + 11w^{2} - 3w - 4]$ | $-\frac{3}{2}e + 7$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{1}{4}e^{2} + e - 13$ |
| 71 | $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 17w^{2} - w - 6]$ | $-e + 6$ |
| 71 | $[71, 71, 2w^{4} - 4w^{3} - 6w^{2} + 7w + 2]$ | $-\frac{1}{4}e^{2} + 2e + 6$ |
| 71 | $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w]$ | $\phantom{-}e - 7$ |
| 71 | $[71, 71, -2w^{5} + 5w^{4} + 6w^{3} - 14w^{2} - 3w + 5]$ | $-1$ |
| 83 | $[83, 83, -3w^{5} + 7w^{4} + 9w^{3} - 17w^{2} - 5w + 5]$ | $-\frac{3}{4}e^{2} + 4e + 11$ |
| 83 | $[83, 83, 3w^{5} - 6w^{4} - 10w^{3} + 12w^{2} + 5w - 2]$ | $-\frac{1}{2}e + 1$ |
| 83 | $[83, 83, -2w^{5} + 5w^{4} + 5w^{3} - 11w^{2} - 3w + 3]$ | $\phantom{-}e - 6$ |
| 83 | $[83, 83, 3w^{5} - 7w^{4} - 8w^{3} + 15w^{2} + 2w - 4]$ | $\phantom{-}\frac{3}{4}e^{2} - 4e - 10$ |
| 97 | $[97, 97, -3w^{5} + 6w^{4} + 10w^{3} - 12w^{2} - 5w + 3]$ | $-4$ |
| 97 | $[97, 97, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w - 3]$ | $\phantom{-}\frac{1}{4}e^{2} - \frac{5}{2}e - 3$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $71$ | $[71,71,-w^{5} + 4w^{4} - 11w^{2} + 2w + 4]$ | $1$ |