Base field 3.3.568.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[25, 5, -w^{2} - w - 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 10x^{6} + x^{5} + 27x^{4} - 7x^{3} - 14x^{2} + 2x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $-\frac{1}{3}e^{7} + \frac{1}{3}e^{6} + 3e^{5} - \frac{10}{3}e^{4} - \frac{20}{3}e^{3} + 9e^{2} + \frac{2}{3}e - \frac{7}{3}$ |
| 5 | $[5, 5, w^{2} - w - 7]$ | $\phantom{-}\frac{1}{3}e^{7} - \frac{1}{3}e^{6} - 4e^{5} + \frac{13}{3}e^{4} + \frac{38}{3}e^{3} - 14e^{2} - \frac{17}{3}e + \frac{10}{3}$ |
| 11 | $[11, 11, -w^{2} + w + 1]$ | $-e^{7} + 10e^{5} - e^{4} - 27e^{3} + 6e^{2} + 14e - 2$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $-\frac{2}{3}e^{7} + \frac{2}{3}e^{6} + 6e^{5} - \frac{14}{3}e^{4} - \frac{46}{3}e^{3} + 8e^{2} + \frac{31}{3}e - \frac{14}{3}$ |
| 25 | $[25, 5, -w^{2} - w - 1]$ | $-1$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}\frac{2}{3}e^{7} + \frac{1}{3}e^{6} - 4e^{5} - \frac{13}{3}e^{4} + \frac{4}{3}e^{3} + 12e^{2} + \frac{17}{3}e - \frac{13}{3}$ |
| 29 | $[29, 29, -w^{2} + 3w - 1]$ | $\phantom{-}\frac{7}{3}e^{7} - \frac{4}{3}e^{6} - 22e^{5} + \frac{34}{3}e^{4} + \frac{161}{3}e^{3} - 27e^{2} - \frac{50}{3}e + \frac{7}{3}$ |
| 37 | $[37, 37, 3w^{2} - 5w - 13]$ | $-4e^{7} - e^{6} + 39e^{5} + 4e^{4} - 99e^{3} + 13e^{2} + 39e - 4$ |
| 41 | $[41, 41, 2w - 1]$ | $\phantom{-}e^{7} + e^{6} - 11e^{5} - 7e^{4} + 33e^{3} + 7e^{2} - 21e - 1$ |
| 53 | $[53, 53, 5w^{2} - 9w - 21]$ | $-\frac{1}{3}e^{7} + \frac{1}{3}e^{6} + 6e^{5} - \frac{22}{3}e^{4} - \frac{74}{3}e^{3} + 29e^{2} + \frac{38}{3}e - \frac{22}{3}$ |
| 53 | $[53, 53, 3w^{2} - 5w - 15]$ | $\phantom{-}2e^{7} - 20e^{5} + e^{4} + 55e^{3} - 9e^{2} - 35e$ |
| 53 | $[53, 53, w^{2} - 3w - 7]$ | $\phantom{-}\frac{2}{3}e^{7} + \frac{4}{3}e^{6} - 7e^{5} - \frac{37}{3}e^{4} + \frac{64}{3}e^{3} + 28e^{2} - \frac{58}{3}e - \frac{28}{3}$ |
| 59 | $[59, 59, w^{2} - 3w - 5]$ | $\phantom{-}\frac{11}{3}e^{7} + \frac{1}{3}e^{6} - 32e^{5} - \frac{13}{3}e^{4} + \frac{205}{3}e^{3} + 5e^{2} - \frac{64}{3}e - \frac{10}{3}$ |
| 61 | $[61, 61, 2w^{2} - 4w - 9]$ | $-\frac{13}{3}e^{7} + \frac{1}{3}e^{6} + 41e^{5} - \frac{13}{3}e^{4} - \frac{296}{3}e^{3} + 22e^{2} + \frac{86}{3}e - \frac{10}{3}$ |
| 61 | $[61, 61, 2w - 7]$ | $-2e^{6} + 2e^{5} + 15e^{4} - 10e^{3} - 25e^{2} + 5e + 6$ |
| 61 | $[61, 61, 2w - 5]$ | $\phantom{-}\frac{2}{3}e^{7} + \frac{4}{3}e^{6} - 5e^{5} - \frac{34}{3}e^{4} + \frac{16}{3}e^{3} + 22e^{2} + \frac{17}{3}e - \frac{19}{3}$ |
| 67 | $[67, 67, -w^{2} + w - 1]$ | $\phantom{-}\frac{4}{3}e^{7} + \frac{2}{3}e^{6} - 14e^{5} - \frac{11}{3}e^{4} + \frac{113}{3}e^{3} + e^{2} - \frac{32}{3}e - \frac{23}{3}$ |
| 71 | $[71, 71, -2w - 5]$ | $\phantom{-}2e^{7} - 18e^{5} - e^{4} + 42e^{3} - e^{2} - 19e + 6$ |
| 71 | $[71, 71, 3w^{2} - 3w - 19]$ | $\phantom{-}\frac{8}{3}e^{7} - \frac{5}{3}e^{6} - 26e^{5} + \frac{47}{3}e^{4} + \frac{199}{3}e^{3} - 42e^{2} - \frac{58}{3}e + \frac{26}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, -w^{2} - w - 1]$ | $1$ |