Base field 4.4.15125.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 14x^{2} + 14x + 31\); narrow class number \(4\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11, 11, 2w^{3} + 3w^{2} - 18w - 16]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 66x^{2} + 900\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, 4w^{3} + 7w^{2} - 37w - 45]$ | $-3$ |
| 11 | $[11, 11, 2w^{3} + 3w^{2} - 18w - 16]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w + 2]$ | $-2$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}0$ |
| 19 | $[19, 19, 4w^{3} + 7w^{2} - 36w - 45]$ | $\phantom{-}e$ |
| 19 | $[19, 19, -w^{3} - w^{2} + 9w + 3]$ | $\phantom{-}\frac{1}{30}e^{3} - \frac{11}{5}e$ |
| 19 | $[19, 19, -2w^{3} - 4w^{2} + 17w + 23]$ | $-\frac{1}{45}e^{3} + \frac{17}{15}e$ |
| 19 | $[19, 19, w^{3} + 2w^{2} - 10w - 10]$ | $-\frac{1}{90}e^{3} + \frac{1}{15}e$ |
| 29 | $[29, 29, -w - 2]$ | $-\frac{1}{45}e^{3} + \frac{17}{15}e$ |
| 29 | $[29, 29, -w^{3} - 2w^{2} + 8w + 15]$ | $-\frac{1}{90}e^{3} + \frac{1}{15}e$ |
| 29 | $[29, 29, 2w^{3} + 3w^{2} - 18w - 20]$ | $\phantom{-}\frac{1}{90}e^{3} - \frac{1}{15}e$ |
| 29 | $[29, 29, -3w^{3} - 5w^{2} + 27w + 28]$ | $\phantom{-}\frac{1}{45}e^{3} - \frac{17}{15}e$ |
| 31 | $[31, 31, 3w^{3} + 5w^{2} - 27w - 31]$ | $-\frac{1}{3}e^{2} + 9$ |
| 31 | $[31, 31, -3w^{3} - 5w^{2} + 27w + 30]$ | $-\frac{1}{3}e^{2} + 9$ |
| 31 | $[31, 31, -2w^{3} - 3w^{2} + 18w + 17]$ | $\phantom{-}\frac{1}{3}e^{2} - 13$ |
| 31 | $[31, 31, 2w^{3} + 3w^{2} - 18w - 18]$ | $\phantom{-}\frac{1}{3}e^{2} - 13$ |
| 71 | $[71, 71, -w^{3} - 2w^{2} + 10w + 8]$ | $-\frac{1}{3}e^{2} + 17$ |
| 71 | $[71, 71, 4w^{3} + 8w^{2} - 35w - 50]$ | $-\frac{2}{3}e^{2} + 21$ |
| 71 | $[71, 71, -4w^{3} - 7w^{2} + 36w + 47]$ | $\phantom{-}\frac{2}{3}e^{2} - 23$ |
| 71 | $[71, 71, -w^{3} - 2w^{2} + 8w + 17]$ | $\phantom{-}\frac{1}{3}e^{2} - 5$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, 2w^{3} + 3w^{2} - 18w - 16]$ | $-1$ |