Base field 5.5.122821.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 4x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[17, 17, -w^{3} + 3w^{2} + w - 3]$ |
| Dimension: | $10$ |
| 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:
| \(x^{10} - 4x^{9} - 17x^{8} + 62x^{7} + 124x^{6} - 326x^{5} - 452x^{4} + 642x^{3} + 683x^{2} - 358x - 227\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{4} - 2w^{3} - 3w^{2} + 2w + 1]$ | $\phantom{-}e$ |
| 8 | $[8, 2, w^{4} - 2w^{3} - 3w^{2} + 3w + 1]$ | $-\frac{1}{64}e^{9} + \frac{7}{64}e^{8} - \frac{1}{16}e^{7} - \frac{25}{32}e^{6} + \frac{29}{32}e^{5} + \frac{7}{8}e^{4} - \frac{9}{16}e^{3} + \frac{85}{32}e^{2} - \frac{137}{64}e - \frac{159}{64}$ |
| 11 | $[11, 11, -w^{2} + w + 2]$ | $\phantom{-}\frac{1}{64}e^{9} - \frac{7}{64}e^{8} + \frac{1}{16}e^{7} + \frac{33}{32}e^{6} - \frac{61}{32}e^{5} - \frac{17}{8}e^{4} + \frac{105}{16}e^{3} - \frac{61}{32}e^{2} - \frac{247}{64}e + \frac{303}{64}$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{1}{32}e^{9} - \frac{7}{32}e^{8} - \frac{1}{8}e^{7} + \frac{49}{16}e^{6} - \frac{25}{16}e^{5} - \frac{57}{4}e^{4} + \frac{67}{8}e^{3} + \frac{355}{16}e^{2} - \frac{223}{32}e - \frac{113}{32}$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} + w - 3]$ | $\phantom{-}1$ |
| 19 | $[19, 19, w^{4} - 2w^{3} - 3w^{2} + w + 2]$ | $-\frac{1}{16}e^{9} + \frac{7}{16}e^{8} - \frac{41}{8}e^{6} + \frac{39}{8}e^{5} + 21e^{4} - \frac{41}{2}e^{3} - \frac{275}{8}e^{2} + \frac{323}{16}e + \frac{249}{16}$ |
| 23 | $[23, 23, w^{4} - 3w^{3} - w^{2} + 5w - 3]$ | $-\frac{13}{64}e^{9} + \frac{75}{64}e^{8} + \frac{19}{16}e^{7} - \frac{445}{32}e^{6} + \frac{57}{32}e^{5} + \frac{433}{8}e^{4} - \frac{261}{16}e^{3} - \frac{2327}{32}e^{2} + \frac{1099}{64}e + \frac{1229}{64}$ |
| 23 | $[23, 23, -w^{3} + 2w^{2} + 2w - 2]$ | $-\frac{5}{32}e^{9} + \frac{27}{32}e^{8} + \frac{11}{8}e^{7} - \frac{177}{16}e^{6} - \frac{47}{16}e^{5} + 48e^{4} + \frac{3}{8}e^{3} - \frac{1171}{16}e^{2} + \frac{51}{32}e + \frac{709}{32}$ |
| 29 | $[29, 29, -w^{4} + 2w^{3} + 4w^{2} - 4w - 1]$ | $-\frac{1}{64}e^{9} + \frac{7}{64}e^{8} - \frac{1}{16}e^{7} - \frac{25}{32}e^{6} + \frac{29}{32}e^{5} + \frac{3}{8}e^{4} + \frac{23}{16}e^{3} + \frac{117}{32}e^{2} - \frac{649}{64}e + \frac{1}{64}$ |
| 37 | $[37, 37, w^{4} - 3w^{3} - w^{2} + 5w]$ | $\phantom{-}\frac{5}{32}e^{9} - \frac{27}{32}e^{8} - \frac{11}{8}e^{7} + \frac{181}{16}e^{6} + \frac{31}{16}e^{5} - \frac{199}{4}e^{4} + \frac{61}{8}e^{3} + \frac{1215}{16}e^{2} - \frac{499}{32}e - \frac{717}{32}$ |
| 47 | $[47, 47, w^{4} - 2w^{3} - 4w^{2} + 3w + 1]$ | $-\frac{3}{64}e^{9} + \frac{21}{64}e^{8} + \frac{1}{16}e^{7} - \frac{123}{32}e^{6} + \frac{63}{32}e^{5} + \frac{133}{8}e^{4} - \frac{79}{16}e^{3} - \frac{913}{32}e^{2} - \frac{107}{64}e + \frac{547}{64}$ |
| 49 | $[49, 7, -2w^{3} + 4w^{2} + 6w - 5]$ | $-\frac{3}{16}e^{9} + \frac{17}{16}e^{8} + \frac{5}{4}e^{7} - \frac{105}{8}e^{6} + \frac{7}{8}e^{5} + \frac{213}{4}e^{4} - \frac{63}{4}e^{3} - \frac{611}{8}e^{2} + \frac{325}{16}e + \frac{459}{16}$ |
| 59 | $[59, 59, -w^{4} + 3w^{3} + w^{2} - 7w + 3]$ | $-\frac{11}{32}e^{9} + \frac{69}{32}e^{8} + \frac{11}{8}e^{7} - \frac{419}{16}e^{6} + \frac{187}{16}e^{5} + \frac{427}{4}e^{4} - \frac{505}{8}e^{3} - \frac{2505}{16}e^{2} + \frac{2245}{32}e + \frac{1507}{32}$ |
| 67 | $[67, 67, w^{3} - 2w^{2} - w + 3]$ | $\phantom{-}\frac{1}{8}e^{9} - \frac{5}{8}e^{8} - \frac{3}{2}e^{7} + \frac{37}{4}e^{6} + \frac{23}{4}e^{5} - \frac{89}{2}e^{4} - \frac{17}{2}e^{3} + \frac{291}{4}e^{2} + \frac{41}{8}e - \frac{175}{8}$ |
| 67 | $[67, 67, -w^{4} + 3w^{3} + 2w^{2} - 6w - 1]$ | $-\frac{13}{64}e^{9} + \frac{75}{64}e^{8} + \frac{19}{16}e^{7} - \frac{437}{32}e^{6} + \frac{9}{32}e^{5} + \frac{431}{8}e^{4} - \frac{101}{16}e^{3} - \frac{2431}{32}e^{2} + \frac{491}{64}e + \frac{1501}{64}$ |
| 71 | $[71, 71, -w^{3} + 3w^{2} + 2w - 4]$ | $-\frac{1}{64}e^{9} + \frac{7}{64}e^{8} - \frac{1}{16}e^{7} - \frac{25}{32}e^{6} + \frac{29}{32}e^{5} + \frac{3}{8}e^{4} + \frac{7}{16}e^{3} + \frac{181}{32}e^{2} - \frac{329}{64}e - \frac{255}{64}$ |
| 83 | $[83, 83, -w^{4} + 3w^{3} + 2w^{2} - 8w - 2]$ | $\phantom{-}\frac{7}{32}e^{9} - \frac{41}{32}e^{8} - \frac{11}{8}e^{7} + \frac{255}{16}e^{6} - \frac{31}{16}e^{5} - \frac{259}{4}e^{4} + \frac{177}{8}e^{3} + \frac{1405}{16}e^{2} - \frac{889}{32}e - \frac{575}{32}$ |
| 83 | $[83, 83, -w^{4} + 3w^{3} + 2w^{2} - 6w - 2]$ | $\phantom{-}\frac{13}{64}e^{9} - \frac{75}{64}e^{8} - \frac{19}{16}e^{7} + \frac{445}{32}e^{6} - \frac{57}{32}e^{5} - \frac{429}{8}e^{4} + \frac{261}{16}e^{3} + \frac{2103}{32}e^{2} - \frac{1035}{64}e - \frac{365}{64}$ |
| 103 | $[103, 103, w^{3} - 3w^{2} - 2w + 2]$ | $-\frac{1}{4}e^{9} + \frac{3}{2}e^{8} + \frac{3}{2}e^{7} - \frac{39}{2}e^{6} + 4e^{5} + \frac{173}{2}e^{4} - \frac{67}{2}e^{3} - \frac{279}{2}e^{2} + \frac{161}{4}e + 43$ |
| 113 | $[113, 113, -2w^{4} + 4w^{3} + 7w^{2} - 7w - 2]$ | $-\frac{23}{64}e^{9} + \frac{129}{64}e^{8} + \frac{41}{16}e^{7} - \frac{815}{32}e^{6} + \frac{27}{32}e^{5} + \frac{841}{8}e^{4} - \frac{511}{16}e^{3} - \frac{4621}{32}e^{2} + \frac{3057}{64}e + \frac{1815}{64}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{3} + 3w^{2} + w - 3]$ | $-1$ |