Base field 6.6.1541581.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 2x^{3} + 9x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[17, 17, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 3w - 3]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $17$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 4x^{5} - 13x^{4} - 41x^{3} + 58x^{2} + 64x - 22\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w + 1]$ | $\phantom{-}\frac{2}{173}e^{5} + \frac{29}{173}e^{4} + \frac{19}{173}e^{3} - \frac{315}{173}e^{2} - \frac{164}{173}e + \frac{136}{173}$ |
| 11 | $[11, 11, w^{2} - w - 2]$ | $-\frac{18}{173}e^{5} - \frac{88}{173}e^{4} + \frac{175}{173}e^{3} + \frac{759}{173}e^{2} - \frac{773}{173}e - \frac{532}{173}$ |
| 17 | $[17, 17, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 3w - 3]$ | $\phantom{-}1$ |
| 27 | $[27, 3, w^{5} - w^{4} - 5w^{3} + w^{2} + 6w + 1]$ | $\phantom{-}\frac{13}{173}e^{5} + \frac{102}{173}e^{4} + \frac{37}{173}e^{3} - \frac{750}{173}e^{2} - \frac{201}{173}e + \frac{192}{173}$ |
| 27 | $[27, 3, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $\phantom{-}\frac{9}{173}e^{5} + \frac{44}{173}e^{4} - \frac{174}{173}e^{3} - \frac{639}{173}e^{2} + \frac{992}{173}e + \frac{958}{173}$ |
| 37 | $[37, 37, -w^{2} + 2w + 2]$ | $\phantom{-}\frac{25}{173}e^{5} + \frac{103}{173}e^{4} - \frac{368}{173}e^{3} - \frac{1083}{173}e^{2} + \frac{1583}{173}e + \frac{662}{173}$ |
| 47 | $[47, 47, -w^{5} + 2w^{4} + 3w^{3} - 3w^{2} - 2w - 1]$ | $-\frac{4}{173}e^{5} - \frac{58}{173}e^{4} - \frac{211}{173}e^{3} + \frac{111}{173}e^{2} + \frac{1539}{173}e + \frac{766}{173}$ |
| 53 | $[53, 53, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} + 3]$ | $-\frac{16}{173}e^{5} - \frac{59}{173}e^{4} + \frac{194}{173}e^{3} + \frac{617}{173}e^{2} - \frac{245}{173}e - \frac{1434}{173}$ |
| 59 | $[59, 59, w^{4} - 2w^{3} - 2w^{2} + 3w - 2]$ | $\phantom{-}e^{2} + e - 10$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{25}{173}e^{5} + \frac{103}{173}e^{4} - \frac{195}{173}e^{3} - \frac{1083}{173}e^{2} - \frac{320}{173}e + \frac{2219}{173}$ |
| 67 | $[67, 67, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w - 2]$ | $\phantom{-}\frac{25}{173}e^{5} + \frac{103}{173}e^{4} - \frac{22}{173}e^{3} - \frac{218}{173}e^{2} - \frac{839}{173}e - \frac{2106}{173}$ |
| 67 | $[67, 67, -w^{5} + 3w^{4} + w^{3} - 7w^{2} + 3w + 2]$ | $-\frac{10}{173}e^{5} + \frac{28}{173}e^{4} + \frac{251}{173}e^{3} - \frac{328}{173}e^{2} - \frac{910}{173}e - \frac{680}{173}$ |
| 71 | $[71, 71, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $\phantom{-}\frac{21}{173}e^{5} + \frac{45}{173}e^{4} - \frac{406}{173}e^{3} - \frac{453}{173}e^{2} + \frac{2084}{173}e + \frac{44}{173}$ |
| 71 | $[71, 71, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $-\frac{28}{173}e^{5} - \frac{60}{173}e^{4} + \frac{426}{173}e^{3} + \frac{431}{173}e^{2} - \frac{1856}{173}e - \frac{866}{173}$ |
| 73 | $[73, 73, 2w^{5} - 4w^{4} - 7w^{3} + 10w^{2} + 5w - 3]$ | $-\frac{33}{173}e^{5} - \frac{219}{173}e^{4} + \frac{119}{173}e^{3} + \frac{1651}{173}e^{2} - \frac{754}{173}e - \frac{514}{173}$ |
| 83 | $[83, 83, w^{4} - 2w^{3} - 4w^{2} + 5w + 2]$ | $-\frac{37}{173}e^{5} - \frac{277}{173}e^{4} - \frac{92}{173}e^{3} + \frac{2281}{173}e^{2} + \frac{1304}{173}e - \frac{2516}{173}$ |
| 83 | $[83, 83, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 3]$ | $\phantom{-}\frac{27}{173}e^{5} + \frac{132}{173}e^{4} - \frac{176}{173}e^{3} - \frac{879}{173}e^{2} + \frac{727}{173}e - \frac{586}{173}$ |
| 89 | $[89, 89, -w^{5} + w^{4} + 6w^{3} - 2w^{2} - 8w + 1]$ | $\phantom{-}\frac{24}{173}e^{5} + \frac{175}{173}e^{4} + \frac{228}{173}e^{3} - \frac{1012}{173}e^{2} - \frac{2314}{173}e + \frac{1286}{173}$ |
| 97 | $[97, 97, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 7w]$ | $\phantom{-}\frac{49}{173}e^{5} + \frac{105}{173}e^{4} - \frac{832}{173}e^{3} - \frac{1057}{173}e^{2} + \frac{3421}{173}e + \frac{1256}{173}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 3w - 3]$ | $-1$ |