Base field 5.5.180769.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 7x^{2} - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[25, 25, w^{4} - 2w^{3} - 3w^{2} + 6w - 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 10x^{2} + 18\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w^{4} - 2w^{3} - 4w^{2} + 6w + 1]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{4} + 2w^{3} + 4w^{2} - 6w]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{10}{3}e$ |
| 7 | $[7, 7, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $\phantom{-}e^{2} - 6$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w]$ | $-\frac{1}{3}e^{3} + \frac{1}{3}e$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $-6$ |
| 32 | $[32, 2, 2]$ | $-3e^{2} + 15$ |
| 37 | $[37, 37, -w^{4} + 2w^{3} + 3w^{2} - 7w + 4]$ | $-\frac{2}{3}e^{3} + \frac{14}{3}e$ |
| 41 | $[41, 41, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $-2e$ |
| 43 | $[43, 43, -w^{4} + 2w^{3} + 4w^{2} - 5w - 3]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{7}{3}e$ |
| 43 | $[43, 43, -w^{2} + w + 3]$ | $\phantom{-}4e^{2} - 18$ |
| 47 | $[47, 47, 2w^{4} - 3w^{3} - 9w^{2} + 8w + 3]$ | $-e^{3} + 9e$ |
| 61 | $[61, 61, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 2]$ | $-\frac{1}{3}e^{3} + \frac{10}{3}e$ |
| 79 | $[79, 79, w^{2} - w - 5]$ | $\phantom{-}\frac{8}{3}e^{3} - \frac{53}{3}e$ |
| 79 | $[79, 79, -w^{3} + 2w^{2} + 3w - 3]$ | $-\frac{7}{3}e^{3} + \frac{46}{3}e$ |
| 79 | $[79, 79, -2w^{4} + 4w^{3} + 7w^{2} - 14w + 2]$ | $-\frac{4}{3}e^{3} + \frac{31}{3}e$ |
| 97 | $[97, 97, w^{3} - 6w]$ | $-\frac{1}{3}e^{3} - \frac{2}{3}e$ |
| 101 | $[101, 101, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ | $\phantom{-}2e^{3} - 13e$ |
| 101 | $[101, 101, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 1]$ | $\phantom{-}0$ |
| 107 | $[107, 107, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 2]$ | $-4e^{2} + 18$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,w^{4}-2w^{3}-4w^{2}+6w+1]$ | $1$ |