Base field 4.4.9301.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[21, 21, -w^{3} + w^{2} + 5w]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 11x^{2} - 6x + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-1$ |
| 5 | $[5, 5, -w^{3} + w^{2} + 4w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $-1$ |
| 7 | $[7, 7, -w^{2} + w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 4e + 2$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 6e - 1$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 4w - 2]$ | $-e^{2} + 6$ |
| 23 | $[23, 23, -w^{3} + 2w^{2} + 3w - 2]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 5e + 4$ |
| 27 | $[27, 3, -w^{3} + w^{2} + 5w - 1]$ | $\phantom{-}e^{2} - e - 2$ |
| 37 | $[37, 37, -w^{3} + 4w + 1]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 7e + 2$ |
| 37 | $[37, 37, -w^{3} + w^{2} + 2w + 1]$ | $-e + 4$ |
| 49 | $[49, 7, -w^{3} + 3w^{2} + 2w - 4]$ | $-e^{2} + 6$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 4w - 2]$ | $\phantom{-}e^{2} - 6$ |
| 61 | $[61, 61, -w^{3} + 3w^{2} + 2w - 7]$ | $\phantom{-}e^{3} - 10e + 2$ |
| 67 | $[67, 67, w^{2} - 3w - 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - e + 8$ |
| 71 | $[71, 71, -w^{2} + 5]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - 5e - 4$ |
| 71 | $[71, 71, 2w^{3} - w^{2} - 9w - 2]$ | $-\frac{3}{2}e^{3} + \frac{3}{2}e^{2} + 12e + 2$ |
| 71 | $[71, 71, w^{2} - 2w - 5]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{5}{2}e^{2} - 2e + 14$ |
| 79 | $[79, 79, w^{2} - 3w - 1]$ | $\phantom{-}\frac{3}{2}e^{3} - \frac{1}{2}e^{2} - 13e$ |
| 79 | $[79, 79, w^{3} - 6w - 1]$ | $\phantom{-}e^{2} - e - 6$ |
| 89 | $[89, 89, -w^{3} + 3w^{2} + 3w - 7]$ | $-e^{3} - e^{2} + 11e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $1$ |
| $7$ | $[7, 7, -w^{2} + 2]$ | $1$ |