Base field 4.4.13068.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[4, 2, w^{3} - w^{2} - 5w - 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 13x^{4} + 43x^{2} - 23\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{3} - w^{2} - 6w - 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w^{3} + 2w^{2} + 4w - 2]$ | $-\frac{1}{4}e^{4} + \frac{5}{2}e^{2} - \frac{13}{4}$ |
| 4 | $[4, 2, w^{3} - w^{2} - 5w - 2]$ | $-1$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ | $-\frac{1}{4}e^{5} + \frac{7}{2}e^{3} - \frac{41}{4}e$ |
| 17 | $[17, 17, -w + 2]$ | $-\frac{1}{4}e^{5} + \frac{7}{2}e^{3} - \frac{41}{4}e$ |
| 29 | $[29, 29, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}e^{3} - 9e$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 4w]$ | $\phantom{-}e^{3} - 9e$ |
| 31 | $[31, 31, -w^{2} + 2]$ | $-e^{4} + 8e^{2} - 9$ |
| 31 | $[31, 31, -w^{3} + 7w + 5]$ | $-e^{4} + 8e^{2} - 9$ |
| 41 | $[41, 41, -2w^{3} + 2w^{2} + 13w - 2]$ | $-\frac{1}{2}e^{5} + 5e^{3} - \frac{21}{2}e$ |
| 41 | $[41, 41, 3w^{3} - 4w^{2} - 17w + 5]$ | $-\frac{1}{2}e^{5} + 5e^{3} - \frac{21}{2}e$ |
| 67 | $[67, 67, 3w^{3} - 4w^{2} - 17w + 1]$ | $-\frac{1}{2}e^{4} + 2e^{2} + \frac{21}{2}$ |
| 67 | $[67, 67, -w^{2} + 4w + 2]$ | $-\frac{1}{2}e^{4} + 2e^{2} + \frac{21}{2}$ |
| 83 | $[83, 83, 2w^{2} - 5w - 2]$ | $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + \frac{25}{2}e$ |
| 83 | $[83, 83, -w^{3} + 8w + 6]$ | $-e^{5} + 9e^{3} - 12e$ |
| 83 | $[83, 83, w^{3} - 2w^{2} - 2w - 2]$ | $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + \frac{25}{2}e$ |
| 83 | $[83, 83, w^{3} - 2w^{2} - 6w]$ | $-e^{5} + 9e^{3} - 12e$ |
| 97 | $[97, 97, -3w^{3} + 2w^{2} + 17w + 7]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{2} - \frac{11}{4}$ |
| 97 | $[97, 97, w^{3} - 4w^{2} + 3w + 1]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{2} - \frac{11}{4}$ |
| 97 | $[97, 97, -5w^{3} + 8w^{2} + 24w - 8]$ | $\phantom{-}\frac{5}{4}e^{4} - \frac{21}{2}e^{2} + \frac{25}{4}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, w^{3} - w^{2} - 5w - 2]$ | $1$ |