Base field 4.4.17069.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} - 4x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 4x^{5} - 4x^{4} - 30x^{3} - 16x^{2} + 40x + 34\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w^{3} - 2w^{2} - 6w + 1]$ | $-e^{4} + 8e^{2} - e - 12$ |
| 9 | $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ | $\phantom{-}1$ |
| 16 | $[16, 2, 2]$ | $-e^{4} + 8e^{2} - 11$ |
| 17 | $[17, 17, w^{3} - w^{2} - 8w - 5]$ | $\phantom{-}2e^{5} + 5e^{4} - 15e^{3} - 38e^{2} + 19e + 50$ |
| 17 | $[17, 17, -2w^{3} + 4w^{2} + 11w - 2]$ | $\phantom{-}e^{5} - 8e^{3} + 10e$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ | $-2e^{5} - 2e^{4} + 15e^{3} + 14e^{2} - 19e - 20$ |
| 17 | $[17, 17, w^{3} - 2w^{2} - 4w + 1]$ | $\phantom{-}e^{5} + 2e^{4} - 8e^{3} - 14e^{2} + 14e + 16$ |
| 25 | $[25, 5, w^{3} - 3w^{2} - 3w + 1]$ | $-5e^{5} - 9e^{4} + 38e^{3} + 64e^{2} - 52e - 80$ |
| 25 | $[25, 5, w^{2} - 2w - 7]$ | $\phantom{-}3e^{5} + 7e^{4} - 22e^{3} - 50e^{2} + 28e + 60$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 6w - 1]$ | $-3e^{5} - 4e^{4} + 22e^{3} + 28e^{2} - 26e - 36$ |
| 29 | $[29, 29, w - 2]$ | $\phantom{-}5e^{5} + 10e^{4} - 38e^{3} - 74e^{2} + 50e + 96$ |
| 53 | $[53, 53, w^{3} - 3w^{2} - 4w + 4]$ | $\phantom{-}2e^{5} + 4e^{4} - 14e^{3} - 27e^{2} + 16e + 32$ |
| 53 | $[53, 53, -w^{3} + 3w^{2} + 4w - 5]$ | $-6e^{5} - 12e^{4} + 46e^{3} + 87e^{2} - 64e - 108$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 7w - 4]$ | $-9e^{5} - 15e^{4} + 70e^{3} + 110e^{2} - 100e - 146$ |
| 61 | $[61, 61, -4w^{3} + 11w^{2} + 14w - 8]$ | $-e^{5} + e^{4} + 10e^{3} - 8e^{2} - 20e + 10$ |
| 101 | $[101, 101, -w^{3} + 2w^{2} + 7w - 1]$ | $\phantom{-}10e^{5} + 12e^{4} - 80e^{3} - 86e^{2} + 120e + 114$ |
| 103 | $[103, 103, -w^{3} + 3w^{2} + 2w - 5]$ | $-5e^{5} - 10e^{4} + 38e^{3} + 71e^{2} - 52e - 82$ |
| 103 | $[103, 103, -w^{3} + w^{2} + 8w + 2]$ | $\phantom{-}3e^{5} + 6e^{4} - 22e^{3} - 41e^{2} + 28e + 50$ |
| 113 | $[113, 113, w^{3} - 3w^{2} - 3w + 7]$ | $\phantom{-}5e^{5} + 4e^{4} - 40e^{3} - 26e^{2} + 57e + 24$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ | $-1$ |