Base field 4.4.17725.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 12x^{2} + 13x + 41\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, 2w^{2} - 2w - 13]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $49$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 2x^{3} - 17x^{2} + 18x + 76\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{3} + 8w + 8]$ | $-e + 1$ |
| 16 | $[16, 2, 2]$ | $-\frac{1}{2}e^{2} + \frac{1}{2}e$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 3$ |
| 19 | $[19, 19, -w^{2} + 6]$ | $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + 4e - 7$ |
| 19 | $[19, 19, -w^{2} + 2w + 5]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{11}{2}e - 2$ |
| 19 | $[19, 19, -w + 2]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 3$ |
| 25 | $[25, 5, 2w^{2} - 2w - 13]$ | $-1$ |
| 29 | $[29, 29, -w^{2} + 9]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - 4e + 13$ |
| 29 | $[29, 29, -w^{2} + 2w + 6]$ | $-\frac{1}{2}e^{3} + e^{2} + \frac{11}{2}e - 3$ |
| 29 | $[29, 29, w^{2} - 7]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 6e + 3$ |
| 29 | $[29, 29, -w^{2} + 2w + 8]$ | $-\frac{1}{2}e^{3} + \frac{11}{2}e + 8$ |
| 31 | $[31, 31, -2w^{2} + w + 12]$ | $\phantom{-}\frac{1}{2}e^{3} - e^{2} - \frac{9}{2}e + 4$ |
| 31 | $[31, 31, 2w^{2} - 3w - 11]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 5e - 1$ |
| 41 | $[41, 41, -w]$ | $\phantom{-}e^{3} - 3e^{2} - 6e + 20$ |
| 41 | $[41, 41, -w + 1]$ | $-e^{3} + 9e + 12$ |
| 49 | $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ | $-\frac{1}{2}e^{3} - 2e^{2} + \frac{15}{2}e + 22$ |
| 49 | $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{7}{2}e^{2} - 2e + 27$ |
| 61 | $[61, 61, 2w^{2} - 3w - 14]$ | $-\frac{1}{2}e^{3} + \frac{7}{2}e^{2} + e - 27$ |
| 61 | $[61, 61, 2w^{2} - w - 15]$ | $\phantom{-}\frac{1}{2}e^{3} + 2e^{2} - \frac{13}{2}e - 23$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, 2w^{2} - 2w - 13]$ | $1$ |