Base field 6.6.1397493.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 3x^{4} + 10x^{3} + 3x^{2} - 6x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $4$ |
| CM: | yes |
| 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:
| \(x^{4} - x^{3} - 12x^{2} + 15x + 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}0$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 4w]$ | $\phantom{-}0$ |
| 19 | $[19, 19, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + w - 4]$ | $-e^{3} - 2e^{2} + 9e + 8$ |
| 19 | $[19, 19, w^{2} - w - 1]$ | $-e^{3} - 2e^{2} + 9e + 8$ |
| 37 | $[37, 37, w^{4} - 2w^{3} - 3w^{2} + 3w + 2]$ | $\phantom{-}2e^{3} + e^{2} - 18e + 2$ |
| 37 | $[37, 37, w^{4} - 4w^{3} + w^{2} + 7w - 3]$ | $\phantom{-}2e^{3} + e^{2} - 18e + 2$ |
| 53 | $[53, 53, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 6]$ | $\phantom{-}0$ |
| 53 | $[53, 53, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 2]$ | $\phantom{-}0$ |
| 64 | $[64, 2, -2]$ | $-e^{3} + e^{2} + 12e - 7$ |
| 71 | $[71, 71, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 3w - 1]$ | $\phantom{-}0$ |
| 71 | $[71, 71, 2w^{5} - 5w^{4} - 8w^{3} + 15w^{2} + 12w - 6]$ | $\phantom{-}0$ |
| 71 | $[71, 71, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 7]$ | $\phantom{-}0$ |
| 73 | $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 16w^{2} - 7w + 3]$ | $\phantom{-}2e^{3} + 4e^{2} - 15e - 22$ |
| 73 | $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 17w^{2} - 6w + 6]$ | $\phantom{-}2e^{3} + 4e^{2} - 15e - 22$ |
| 89 | $[89, 89, w^{5} - 2w^{4} - 5w^{3} + 6w^{2} + 8w - 4]$ | $\phantom{-}0$ |
| 89 | $[89, 89, w^{5} - w^{4} - 9w^{3} + 7w^{2} + 16w - 6]$ | $\phantom{-}0$ |
| 89 | $[89, 89, 2w^{5} - 6w^{4} - 4w^{3} + 15w^{2} + 3w - 3]$ | $\phantom{-}0$ |
| 89 | $[89, 89, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 10w - 6]$ | $\phantom{-}0$ |
| 107 | $[107, 107, w^{5} - 2w^{4} - 7w^{3} + 10w^{2} + 12w - 6]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).