Base field 4.4.16357.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, w^{2} + w - 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 12x^{4} + 33x^{2} + 3x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{3} + 5w + 2]$ | $-1$ |
| 5 | $[5, 5, w - 1]$ | $-1$ |
| 11 | $[11, 11, -w^{3} + 5w]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{1}{3}e^{4} - \frac{14}{3}e^{3} + \frac{8}{3}e^{2} + \frac{43}{3}e + \frac{2}{3}$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 6w - 3]$ | $\phantom{-}e^{2} - 2$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{1}{3}e^{4} - \frac{11}{3}e^{3} + \frac{8}{3}e^{2} + \frac{28}{3}e + \frac{2}{3}$ |
| 19 | $[19, 19, 2w^{3} - w^{2} - 11w + 2]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{1}{3}e^{4} - \frac{11}{3}e^{3} + \frac{8}{3}e^{2} + \frac{28}{3}e + \frac{2}{3}$ |
| 25 | $[25, 5, -w^{2} + w + 3]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{1}{3}e^{4} - \frac{14}{3}e^{3} + \frac{5}{3}e^{2} + \frac{43}{3}e + \frac{11}{3}$ |
| 27 | $[27, 3, w^{3} - w^{2} - 5w + 4]$ | $-e^{2} + e + 4$ |
| 31 | $[31, 31, -w - 3]$ | $\phantom{-}\frac{4}{3}e^{5} - \frac{1}{3}e^{4} - \frac{44}{3}e^{3} + \frac{8}{3}e^{2} + \frac{103}{3}e + \frac{2}{3}$ |
| 37 | $[37, 37, -w^{3} - w^{2} + 6w + 4]$ | $-\frac{2}{3}e^{5} - \frac{1}{3}e^{4} + \frac{25}{3}e^{3} + \frac{11}{3}e^{2} - \frac{74}{3}e - \frac{13}{3}$ |
| 41 | $[41, 41, w^{3} + w^{2} - 6w - 5]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{1}{3}e^{4} - \frac{14}{3}e^{3} + \frac{8}{3}e^{2} + \frac{43}{3}e - \frac{7}{3}$ |
| 43 | $[43, 43, w^{3} - 7w - 2]$ | $\phantom{-}\frac{4}{3}e^{5} - \frac{1}{3}e^{4} - \frac{53}{3}e^{3} + \frac{8}{3}e^{2} + \frac{160}{3}e + \frac{8}{3}$ |
| 47 | $[47, 47, -2w^{3} + 11w + 2]$ | $\phantom{-}e^{5} + e^{4} - 11e^{3} - 7e^{2} + 28e + 6$ |
| 61 | $[61, 61, w^{2} - 3]$ | $\phantom{-}\frac{5}{3}e^{5} + \frac{1}{3}e^{4} - \frac{55}{3}e^{3} - \frac{2}{3}e^{2} + \frac{125}{3}e - \frac{8}{3}$ |
| 67 | $[67, 67, w^{2} + w - 4]$ | $\phantom{-}\frac{1}{3}e^{5} + \frac{2}{3}e^{4} - \frac{14}{3}e^{3} - \frac{10}{3}e^{2} + \frac{49}{3}e - \frac{19}{3}$ |
| 79 | $[79, 79, -4w^{3} + 2w^{2} + 22w - 9]$ | $-\frac{1}{3}e^{5} + \frac{1}{3}e^{4} + \frac{11}{3}e^{3} - \frac{5}{3}e^{2} - \frac{25}{3}e + \frac{4}{3}$ |
| 97 | $[97, 97, -3w^{3} + 2w^{2} + 19w - 6]$ | $\phantom{-}2e^{5} - 26e^{3} + 80e + 3$ |
| 97 | $[97, 97, -w^{3} + 6w - 3]$ | $-\frac{2}{3}e^{5} - \frac{1}{3}e^{4} + \frac{22}{3}e^{3} + \frac{8}{3}e^{2} - \frac{65}{3}e - \frac{16}{3}$ |
| 97 | $[97, 97, -3w^{3} + 16w]$ | $\phantom{-}e^{5} - e^{4} - 11e^{3} + 8e^{2} + 28e + 1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w^{3} + 5w + 2]$ | $1$ |
| $5$ | $[5, 5, w - 1]$ | $1$ |