Base field 4.4.13725.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 13x^{2} + x + 31\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 3, -2w^{3} + 6w^{2} + 13w - 26]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 37x^{2} + 304\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -2w^{3} + 6w^{2} + 13w - 26]$ | $-1$ |
| 11 | $[11, 11, w^{2} - w - 8]$ | $-e$ |
| 11 | $[11, 11, -4w^{3} + 13w^{2} + 23w - 55]$ | $\phantom{-}e$ |
| 16 | $[16, 2, 2]$ | $-\frac{2}{3}e^{2} + \frac{43}{3}$ |
| 19 | $[19, 19, -w - 1]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{8}{3}$ |
| 19 | $[19, 19, -w^{3} + 3w^{2} + 7w - 14]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{8}{3}$ |
| 19 | $[19, 19, w^{3} - 4w^{2} - 5w + 20]$ | $\phantom{-}4$ |
| 19 | $[19, 19, -3w^{3} + 10w^{2} + 17w - 43]$ | $\phantom{-}4$ |
| 25 | $[25, 5, -w^{3} + 3w^{2} + 6w - 10]$ | $\phantom{-}e^{2} - 22$ |
| 29 | $[29, 29, 4w^{3} - 13w^{2} - 23w + 57]$ | $-e$ |
| 29 | $[29, 29, w^{2} - w - 6]$ | $\phantom{-}e$ |
| 31 | $[31, 31, -2w^{3} + 7w^{2} + 11w - 31]$ | $-\frac{1}{3}e^{2} + \frac{20}{3}$ |
| 31 | $[31, 31, -2w^{3} + 7w^{2} + 11w - 32]$ | $-\frac{1}{3}e^{2} + \frac{20}{3}$ |
| 41 | $[41, 41, 3w^{3} - 10w^{2} - 18w + 43]$ | $\phantom{-}2e$ |
| 41 | $[41, 41, 3w^{3} - 9w^{2} - 19w + 37]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{17}{3}e$ |
| 41 | $[41, 41, 2w^{3} - 6w^{2} - 11w + 24]$ | $-\frac{1}{3}e^{3} + \frac{17}{3}e$ |
| 41 | $[41, 41, -2w^{3} + 7w^{2} + 12w - 33]$ | $-2e$ |
| 59 | $[59, 59, 3w^{3} - 10w^{2} - 17w + 46]$ | $\phantom{-}0$ |
| 59 | $[59, 59, -w^{3} + 4w^{2} + 5w - 17]$ | $\phantom{-}0$ |
| 61 | $[61, 61, 4w^{3} - 12w^{2} - 25w + 50]$ | $-2e^{2} + 34$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, -2w^{3} + 6w^{2} + 13w - 26]$ | $1$ |