Base field 3.3.785.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[25, 5, w^{2} + 2w]$ |
| Dimension: | $6$ |
| 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:
| \(x^{6} - 2x^{5} - 11x^{4} + 16x^{3} + 28x^{2} - 12x - 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $-1$ |
| 5 | $[5, 5, -w + 3]$ | $\phantom{-}1$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{2}e^{5} - e^{4} - \frac{9}{2}e^{3} + 7e^{2} + 6e - 3$ |
| 9 | $[9, 3, w^{2} + w - 4]$ | $-e^{2} + 4$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{9}{2}e^{2} - e + 5$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{3}{2}e^{4} - \frac{9}{2}e^{3} + \frac{25}{2}e^{2} + 6e - 7$ |
| 23 | $[23, 23, w^{2} - 2]$ | $-\frac{1}{2}e^{5} + \frac{3}{2}e^{4} + \frac{7}{2}e^{3} - \frac{25}{2}e^{2} + 2e + 13$ |
| 23 | $[23, 23, w^{2} - 3]$ | $\phantom{-}2e + 2$ |
| 23 | $[23, 23, -w^{2} + 8]$ | $-\frac{1}{2}e^{5} + \frac{1}{2}e^{4} + \frac{11}{2}e^{3} - \frac{7}{2}e^{2} - 14e + 3$ |
| 29 | $[29, 29, w - 4]$ | $-e^{4} + e^{3} + 8e^{2} - 5e - 6$ |
| 37 | $[37, 37, w^{2} + w - 8]$ | $\phantom{-}2e^{2} - 2e - 8$ |
| 41 | $[41, 41, w^{2} + 2w - 4]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} + e + 9$ |
| 47 | $[47, 47, 2w^{2} + w - 8]$ | $\phantom{-}\frac{1}{2}e^{4} + e^{3} - \frac{9}{2}e^{2} - 9e + 3$ |
| 59 | $[59, 59, -2w^{2} - 3w + 6]$ | $-\frac{1}{2}e^{4} + \frac{9}{2}e^{2} + e - 1$ |
| 61 | $[61, 61, -2w - 1]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{3}{2}e^{4} - \frac{9}{2}e^{3} + \frac{25}{2}e^{2} + 8e - 9$ |
| 67 | $[67, 67, -2w - 3]$ | $-e^{3} + 10e$ |
| 79 | $[79, 79, 2w^{2} - 9]$ | $\phantom{-}e^{5} - \frac{5}{2}e^{4} - 9e^{3} + \frac{41}{2}e^{2} + 9e - 17$ |
| 109 | $[109, 109, w^{2} + 2w - 6]$ | $-e^{5} + 2e^{4} + 9e^{3} - 15e^{2} - 6e + 4$ |
| 109 | $[109, 109, 2w^{2} + w - 14]$ | $-e^{5} + e^{4} + 12e^{3} - 8e^{2} - 29e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w]$ | $1$ |
| $5$ | $[5, 5, -w + 3]$ | $-1$ |