Base field 5.5.186037.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 2x^{2} + 5x - 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[26, 26, w^{3} - 2w^{2} - 3w + 4]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 7x^{5} + 5x^{4} + 38x^{3} - 25x^{2} - 67x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w^{4} - w^{3} - 6w^{2} + w + 5]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{4} + w^{3} + 6w^{2} - w - 3]$ | $-1$ |
| 16 | $[16, 2, w^{4} - w^{3} - 6w^{2} + 2w + 5]$ | $-\frac{1}{9}e^{5} + \frac{8}{9}e^{4} - \frac{16}{9}e^{3} - \frac{13}{9}e^{2} + \frac{62}{9}e - \frac{13}{9}$ |
| 19 | $[19, 19, -w^{4} + 7w^{2} + 2w - 3]$ | $-\frac{1}{9}e^{5} + \frac{14}{9}e^{4} - \frac{46}{9}e^{3} - \frac{10}{9}e^{2} + \frac{128}{9}e + \frac{32}{9}$ |
| 23 | $[23, 23, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}\frac{1}{9}e^{5} - \frac{11}{9}e^{4} + \frac{31}{9}e^{3} + \frac{7}{9}e^{2} - \frac{68}{9}e + \frac{4}{9}$ |
| 23 | $[23, 23, -w^{4} + 7w^{2} + 4w - 7]$ | $-\frac{1}{9}e^{5} + \frac{5}{9}e^{4} + \frac{8}{9}e^{3} - \frac{46}{9}e^{2} - \frac{7}{9}e + \frac{68}{9}$ |
| 25 | $[25, 5, -w^{2} + w + 3]$ | $\phantom{-}\frac{2}{9}e^{5} - \frac{13}{9}e^{4} + \frac{14}{9}e^{3} + \frac{38}{9}e^{2} - \frac{61}{9}e + \frac{2}{9}$ |
| 31 | $[31, 31, w^{2} - w - 1]$ | $\phantom{-}\frac{5}{9}e^{5} - \frac{37}{9}e^{4} + \frac{56}{9}e^{3} + \frac{98}{9}e^{2} - \frac{187}{9}e - \frac{88}{9}$ |
| 31 | $[31, 31, w^{4} - 6w^{2} - 2w + 3]$ | $-\frac{1}{9}e^{5} + \frac{8}{9}e^{4} - \frac{19}{9}e^{3} + \frac{2}{9}e^{2} + \frac{38}{9}e + \frac{8}{9}$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 4w + 3]$ | $-\frac{4}{9}e^{5} + \frac{29}{9}e^{4} - \frac{34}{9}e^{3} - \frac{106}{9}e^{2} + \frac{110}{9}e + \frac{104}{9}$ |
| 67 | $[67, 67, 2w^{3} - 3w^{2} - 8w + 3]$ | $\phantom{-}\frac{4}{9}e^{5} - \frac{26}{9}e^{4} + \frac{22}{9}e^{3} + \frac{79}{9}e^{2} - \frac{62}{9}e + \frac{28}{9}$ |
| 79 | $[79, 79, -w^{4} + 6w^{2} + 3w - 1]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{4}{3}e^{4} - 2e^{3} + \frac{13}{3}e^{2} + \frac{35}{3}e + 4$ |
| 83 | $[83, 83, 2w^{4} - 14w^{2} - 7w + 11]$ | $\phantom{-}\frac{4}{9}e^{5} - \frac{26}{9}e^{4} + \frac{25}{9}e^{3} + \frac{73}{9}e^{2} - \frac{56}{9}e - \frac{20}{9}$ |
| 83 | $[83, 83, w^{4} - 2w^{3} - 4w^{2} + 6w + 1]$ | $\phantom{-}\frac{4}{9}e^{5} - \frac{26}{9}e^{4} + \frac{19}{9}e^{3} + \frac{76}{9}e^{2} - \frac{14}{9}e + \frac{4}{9}$ |
| 83 | $[83, 83, -w^{4} + 8w^{2} + 3w - 7]$ | $\phantom{-}\frac{5}{9}e^{5} - \frac{43}{9}e^{4} + \frac{86}{9}e^{3} + \frac{68}{9}e^{2} - \frac{199}{9}e + \frac{20}{9}$ |
| 97 | $[97, 97, w^{4} - 2w^{3} - 4w^{2} + 4w + 1]$ | $\phantom{-}\frac{1}{9}e^{5} - \frac{5}{9}e^{4} + \frac{7}{9}e^{3} - \frac{38}{9}e^{2} + \frac{82}{9}e + \frac{142}{9}$ |
| 101 | $[101, 101, 2w^{4} - 14w^{2} - 6w + 11]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{10}{3}e^{4} + \frac{22}{3}e^{3} + \frac{23}{3}e^{2} - \frac{56}{3}e - \frac{10}{3}$ |
| 101 | $[101, 101, -w^{4} + 8w^{2} + 2w - 9]$ | $-\frac{4}{9}e^{5} + \frac{41}{9}e^{4} - \frac{106}{9}e^{3} - \frac{58}{9}e^{2} + \frac{290}{9}e + \frac{62}{9}$ |
| 107 | $[107, 107, -w^{3} + 2w^{2} + 4w - 1]$ | $\phantom{-}\frac{1}{9}e^{5} - \frac{11}{9}e^{4} + \frac{13}{9}e^{3} + \frac{88}{9}e^{2} - \frac{86}{9}e - \frac{104}{9}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |
| $13$ | $[13, 13, -w^{4} + w^{3} + 6w^{2} - w - 3]$ | $1$ |