Base field 4.4.4205.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} - x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[53, 53, 2w^{3} - 2w^{2} - 8w - 3]$ |
| 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:
| \(x^{4} - 2x^{3} - 10x^{2} + 4x + 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{3} + w^{2} + 5w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{3} + 2w^{2} + 3w - 3]$ | $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + 3e - 1$ |
| 7 | $[7, 7, w^{3} - 2w^{2} - 3w]$ | $-\frac{1}{2}e^{2} + e + 2$ |
| 13 | $[13, 13, -w^{2} + w + 3]$ | $-\frac{1}{2}e^{2} + 2e + 2$ |
| 13 | $[13, 13, -w^{2} + w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} - e^{2} - 4e + 2$ |
| 16 | $[16, 2, 2]$ | $-e + 5$ |
| 23 | $[23, 23, -w^{2} + 3w + 1]$ | $\phantom{-}e^{2} - e - 6$ |
| 23 | $[23, 23, -2w^{3} + 3w^{2} + 9w - 2]$ | $\phantom{-}\frac{1}{2}e^{3} - 2e^{2} - 3e + 6$ |
| 25 | $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ | $-\frac{1}{2}e^{3} + 2e^{2} + 2e - 4$ |
| 49 | $[49, 7, w^{3} - w^{2} - 6w - 1]$ | $-e^{3} + \frac{5}{2}e^{2} + 5e - 7$ |
| 53 | $[53, 53, 2w^{3} - 2w^{2} - 8w - 3]$ | $-1$ |
| 53 | $[53, 53, 2w^{3} - 2w^{2} - 8w - 1]$ | $\phantom{-}\frac{3}{2}e^{2} - 3e - 9$ |
| 67 | $[67, 67, 2w^{3} - 4w^{2} - 7w + 2]$ | $-e^{3} + 2e^{2} + 6e - 4$ |
| 67 | $[67, 67, -2w^{3} + 4w^{2} + 6w - 1]$ | $\phantom{-}\frac{3}{2}e^{3} - 5e^{2} - 9e + 14$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{1}{2}e^{3} - e^{2} - 8e + 4$ |
| 83 | $[83, 83, 2w^{3} - 3w^{2} - 6w - 1]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 5e - 3$ |
| 83 | $[83, 83, 3w^{3} - 4w^{2} - 12w + 1]$ | $-\frac{1}{2}e^{3} + 2e^{2} + 3e - 6$ |
| 103 | $[103, 103, 3w^{3} - 4w^{2} - 12w - 1]$ | $\phantom{-}e^{3} - 5e^{2} - e + 20$ |
| 103 | $[103, 103, 2w^{3} - 3w^{2} - 6w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} - 3e^{2} - 2e + 8$ |
| 107 | $[107, 107, w^{3} - w^{2} - 3w - 3]$ | $-2e + 12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $53$ | $[53, 53, 2w^{3} - 2w^{2} - 8w - 3]$ | $1$ |