Base field 3.3.1345.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[25, 5, w^{2} - 2w - 3]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 3x^{4} - 13x^{3} - 17x^{2} + 21x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w - 1]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w + 2]$ | $\phantom{-}\frac{4}{9}e^{4} + \frac{14}{9}e^{3} - 5e^{2} - \frac{86}{9}e + \frac{32}{9}$ |
| 7 | $[7, 7, -w + 1]$ | $-\frac{5}{9}e^{4} - \frac{16}{9}e^{3} + \frac{20}{3}e^{2} + \frac{97}{9}e - \frac{64}{9}$ |
| 8 | $[8, 2, 2]$ | $-\frac{1}{9}e^{4} - \frac{2}{9}e^{3} + \frac{5}{3}e^{2} + \frac{2}{9}e - \frac{41}{9}$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $-\frac{1}{9}e^{4} - \frac{5}{9}e^{3} + \frac{4}{3}e^{2} + \frac{41}{9}e - \frac{38}{9}$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $-\frac{2}{9}e^{4} - \frac{10}{9}e^{3} + \frac{5}{3}e^{2} + \frac{82}{9}e - \frac{4}{9}$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $\phantom{-}e^{4} + \frac{10}{3}e^{3} - \frac{35}{3}e^{2} - \frac{64}{3}e + \frac{32}{3}$ |
| 27 | $[27, 3, 3]$ | $-\frac{2}{9}e^{4} - \frac{4}{9}e^{3} + \frac{10}{3}e^{2} + \frac{13}{9}e - \frac{64}{9}$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $-\frac{2}{3}e^{4} - \frac{7}{3}e^{3} + 7e^{2} + \frac{37}{3}e - \frac{10}{3}$ |
| 31 | $[31, 31, w^{2} - w - 8]$ | $\phantom{-}\frac{2}{9}e^{4} + \frac{7}{9}e^{3} - 3e^{2} - \frac{61}{9}e + \frac{52}{9}$ |
| 37 | $[37, 37, -w - 4]$ | $\phantom{-}\frac{5}{3}e^{4} + \frac{17}{3}e^{3} - \frac{59}{3}e^{2} - \frac{110}{3}e + 18$ |
| 43 | $[43, 43, 2w^{2} - 4w - 3]$ | $-\frac{7}{9}e^{4} - \frac{23}{9}e^{3} + \frac{26}{3}e^{2} + \frac{131}{9}e - \frac{44}{9}$ |
| 47 | $[47, 47, w^{2} - 3]$ | $\phantom{-}\frac{1}{9}e^{4} - \frac{1}{9}e^{3} - 3e^{2} + \frac{19}{9}e + \frac{44}{9}$ |
| 53 | $[53, 53, 2w^{2} - w - 11]$ | $\phantom{-}\frac{11}{9}e^{4} + \frac{34}{9}e^{3} - 15e^{2} - \frac{205}{9}e + \frac{142}{9}$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $-\frac{5}{3}e^{4} - 6e^{3} + \frac{55}{3}e^{2} + 40e - \frac{44}{3}$ |
| 67 | $[67, 67, w^{2} + w - 8]$ | $-\frac{8}{9}e^{4} - \frac{25}{9}e^{3} + \frac{31}{3}e^{2} + \frac{124}{9}e - \frac{148}{9}$ |
| 71 | $[71, 71, w^{2} + w - 11]$ | $-\frac{4}{9}e^{4} - \frac{8}{9}e^{3} + \frac{20}{3}e^{2} + \frac{26}{9}e - \frac{56}{9}$ |
| 73 | $[73, 73, -w^{2} + 4w - 2]$ | $-\frac{2}{3}e^{4} - \frac{7}{3}e^{3} + 8e^{2} + \frac{55}{3}e - \frac{34}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w - 1]$ | $-1$ |
| $5$ | $[5, 5, w + 2]$ | $-1$ |