Base field 4.4.16997.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, -w^{3} + 4w]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $39$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 3x^{4} - 7x^{3} + 21x^{2} + 2x - 10\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w]$ | $-1$ |
| 5 | $[5, 5, -w^{2} + w + 2]$ | $-1$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $\phantom{-}e^{2} - e - 6$ |
| 13 | $[13, 13, w^{2} - w - 4]$ | $\phantom{-}\frac{1}{2}e^{4} - e^{3} - \frac{9}{2}e^{2} + 7e + 3$ |
| 16 | $[16, 2, 2]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{7}{2}e^{2} - 5e - 2$ |
| 19 | $[19, 19, -w^{2} + w + 1]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{5}{2}e^{2} - 5e + 2$ |
| 23 | $[23, 23, -w^{3} + 4w + 2]$ | $\phantom{-}\frac{1}{2}e^{4} - e^{3} - \frac{7}{2}e^{2} + 5e + 1$ |
| 25 | $[25, 5, -w^{3} + w^{2} + 3w - 1]$ | $-e^{3} + 6e + 4$ |
| 29 | $[29, 29, w^{3} - w^{2} - 4w + 1]$ | $-e^{3} + 2e^{2} + 7e - 5$ |
| 29 | $[29, 29, -w + 3]$ | $-\frac{1}{2}e^{4} + 2e^{3} + \frac{5}{2}e^{2} - 11e + 1$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 5w - 2]$ | $-e^{3} + 8e + 3$ |
| 37 | $[37, 37, w^{3} - 4w - 1]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{11}{2}e^{2} - 6e - 8$ |
| 37 | $[37, 37, w^{3} - 3w + 1]$ | $\phantom{-}e^{4} - 2e^{3} - 8e^{2} + 11e + 6$ |
| 53 | $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ | $-e^{4} + 2e^{3} + 8e^{2} - 14e - 4$ |
| 59 | $[59, 59, w^{2} + w - 4]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{9}{2}e^{2} - 7e - 4$ |
| 61 | $[61, 61, -2w^{2} + w + 8]$ | $\phantom{-}e^{3} - 2e^{2} - 4e + 7$ |
| 73 | $[73, 73, -w^{3} + 5w - 1]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{13}{2}e^{2} + 14$ |
| 79 | $[79, 79, 2w^{2} + w - 6]$ | $-\frac{1}{2}e^{4} + 2e^{3} + \frac{3}{2}e^{2} - 10e + 5$ |
| 79 | $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ | $-2e^{3} + 2e^{2} + 13e - 7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w]$ | $1$ |
| $5$ | $[5, 5, -w^{2} + w + 2]$ | $1$ |