Base field 6.6.1081856.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - 2x^{3} + 7x^{2} + 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[25, 5, -w^{3} + w^{2} + 4w]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 3x^{3} - 14x^{2} - 11x + 22\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{4} - w^{3} - 4w^{2} + w + 1]$ | $\phantom{-}e$ |
| 8 | $[8, 2, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 5w]$ | $\phantom{-}\frac{1}{37}e^{3} - \frac{9}{37}e^{2} - \frac{54}{37}e + \frac{8}{37}$ |
| 17 | $[17, 17, -w^{2} + w + 2]$ | $-\frac{12}{37}e^{3} - \frac{40}{37}e^{2} + \frac{130}{37}e + \frac{52}{37}$ |
| 23 | $[23, 23, -w^{4} + 2w^{3} + 3w^{2} - 4w - 1]$ | $\phantom{-}\frac{2}{37}e^{3} + \frac{19}{37}e^{2} + \frac{40}{37}e - \frac{206}{37}$ |
| 25 | $[25, 5, -w^{3} + w^{2} + 4w]$ | $\phantom{-}1$ |
| 31 | $[31, 31, -w^{3} + 4w + 1]$ | $-\frac{9}{37}e^{3} - \frac{30}{37}e^{2} + \frac{79}{37}e - \frac{72}{37}$ |
| 31 | $[31, 31, w^{5} - 6w^{3} - w^{2} + 5w]$ | $\phantom{-}\frac{14}{37}e^{3} + \frac{22}{37}e^{2} - \frac{238}{37}e - \frac{36}{37}$ |
| 41 | $[41, 41, -w^{5} + w^{4} + 5w^{3} - 2w^{2} - 6w - 1]$ | $-2$ |
| 47 | $[47, 47, -w^{5} + w^{4} + 6w^{3} - 4w^{2} - 8w + 2]$ | $-\frac{24}{37}e^{3} - \frac{80}{37}e^{2} + \frac{223}{37}e + \frac{252}{37}$ |
| 49 | $[49, 7, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 3]$ | $\phantom{-}\frac{27}{37}e^{3} + \frac{90}{37}e^{2} - \frac{311}{37}e - \frac{228}{37}$ |
| 71 | $[71, 71, -w^{4} + 5w^{2} + w - 3]$ | $-\frac{8}{37}e^{3} - \frac{2}{37}e^{2} + \frac{210}{37}e + \frac{84}{37}$ |
| 71 | $[71, 71, w^{4} - 5w^{2} - 2w + 4]$ | $\phantom{-}\frac{18}{37}e^{3} + \frac{97}{37}e^{2} - \frac{84}{37}e - \frac{596}{37}$ |
| 73 | $[73, 73, -2w^{5} + w^{4} + 10w^{3} - 9w - 1]$ | $\phantom{-}\frac{15}{37}e^{3} + \frac{50}{37}e^{2} - \frac{181}{37}e - \frac{250}{37}$ |
| 73 | $[73, 73, -w^{5} + 6w^{3} + 2w^{2} - 5w - 1]$ | $-\frac{6}{37}e^{3} - \frac{20}{37}e^{2} + \frac{28}{37}e - \frac{122}{37}$ |
| 79 | $[79, 79, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 3]$ | $\phantom{-}\frac{40}{37}e^{3} + \frac{158}{37}e^{2} - \frac{310}{37}e - \frac{420}{37}$ |
| 89 | $[89, 89, w^{5} - 7w^{3} - w^{2} + 9w]$ | $-\frac{15}{37}e^{3} - \frac{50}{37}e^{2} + \frac{33}{37}e + \frac{28}{37}$ |
| 97 | $[97, 97, 2w^{5} - 2w^{4} - 10w^{3} + 5w^{2} + 10w - 1]$ | $-\frac{23}{37}e^{3} - \frac{52}{37}e^{2} + \frac{391}{37}e - \frac{36}{37}$ |
| 103 | $[103, 103, w^{5} - w^{4} - 4w^{3} + w^{2} + 3w + 2]$ | $-\frac{22}{37}e^{3} - \frac{98}{37}e^{2} + \frac{189}{37}e + \frac{342}{37}$ |
| 103 | $[103, 103, -2w^{5} + w^{4} + 11w^{3} - w^{2} - 11w - 1]$ | $-\frac{12}{37}e^{3} + \frac{34}{37}e^{2} + \frac{352}{37}e - \frac{244}{37}$ |
| 103 | $[103, 103, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ | $-\frac{6}{37}e^{3} - \frac{20}{37}e^{2} + \frac{65}{37}e - \frac{122}{37}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, -w^{3} + w^{2} + 4w]$ | $-1$ |