Base field 3.3.985.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[17, 17, -w^{2} + w + 4]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 23x^{8} - 2x^{7} + 172x^{6} + 4x^{5} - 450x^{4} + 167x^{3} + 352x^{2} - 283x + 58\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}\frac{499}{757}e^{9} + \frac{182}{757}e^{8} - \frac{11400}{757}e^{7} - \frac{5297}{757}e^{6} + \frac{83849}{757}e^{5} + \frac{35054}{757}e^{4} - \frac{212631}{757}e^{3} - \frac{6306}{757}e^{2} + \frac{177755}{757}e - \frac{64004}{757}$ |
| 7 | $[7, 7, -w + 2]$ | $\phantom{-}\frac{437}{757}e^{9} + \frac{214}{757}e^{8} - \frac{9844}{757}e^{7} - \frac{5854}{757}e^{6} + \frac{70591}{757}e^{5} + \frac{38572}{757}e^{4} - \frac{169966}{757}e^{3} - \frac{19194}{757}e^{2} + \frac{138774}{757}e - \frac{45044}{757}$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{739}{757}e^{9} + \frac{400}{757}e^{8} - \frac{16886}{757}e^{7} - \frac{10369}{757}e^{6} + \frac{123449}{757}e^{5} + \frac{65928}{757}e^{4} - \frac{307336}{757}e^{3} - \frac{26354}{757}e^{2} + \frac{257247}{757}e - \frac{90781}{757}$ |
| 11 | $[11, 11, -w^{2} + 2w + 2]$ | $-\frac{353}{757}e^{9} - \frac{62}{757}e^{8} + \frac{8151}{757}e^{7} + \frac{2262}{757}e^{6} - \frac{61273}{757}e^{5} - \frac{14670}{757}e^{4} + \frac{162368}{757}e^{3} - \frac{15529}{757}e^{2} - \frac{137144}{757}e + \frac{56376}{757}$ |
| 17 | $[17, 17, -w - 3]$ | $-\frac{1238}{757}e^{9} - \frac{582}{757}e^{8} + \frac{28286}{757}e^{7} + \frac{15666}{757}e^{6} - \frac{207298}{757}e^{5} - \frac{100982}{757}e^{4} + \frac{519210}{757}e^{3} + \frac{33417}{757}e^{2} - \frac{428946}{757}e + \frac{152514}{757}$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{2087}{757}e^{9} + \frac{1145}{757}e^{8} - \frac{47371}{757}e^{7} - \frac{30126}{757}e^{6} + \frac{342084}{757}e^{5} + \frac{195002}{757}e^{4} - \frac{828349}{757}e^{3} - \frac{97978}{757}e^{2} + \frac{674305}{757}e - \frac{228852}{757}$ |
| 17 | $[17, 17, -w^{2} + w + 4]$ | $\phantom{-}1$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}\frac{291}{757}e^{9} + \frac{94}{757}e^{8} - \frac{6595}{757}e^{7} - \frac{2819}{757}e^{6} + \frac{48015}{757}e^{5} + \frac{18188}{757}e^{4} - \frac{119703}{757}e^{3} + \frac{3398}{757}e^{2} + \frac{98163}{757}e - \frac{38930}{757}$ |
| 27 | $[27, 3, -3]$ | $\phantom{-}\frac{120}{757}e^{9} + \frac{109}{757}e^{8} - \frac{2743}{757}e^{7} - \frac{2536}{757}e^{6} + \frac{19800}{757}e^{5} + \frac{15437}{757}e^{4} - \frac{47731}{757}e^{3} - \frac{9267}{757}e^{2} + \frac{42017}{757}e - \frac{16038}{757}$ |
| 29 | $[29, 29, w^{2} - w - 8]$ | $\phantom{-}\frac{390}{757}e^{9} + \frac{165}{757}e^{8} - \frac{9104}{757}e^{7} - \frac{4457}{757}e^{6} + \frac{68892}{757}e^{5} + \frac{28785}{757}e^{4} - \frac{182567}{757}e^{3} - \frac{8354}{757}e^{2} + \frac{155291}{757}e - \frac{50988}{757}$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $\phantom{-}\frac{240}{757}e^{9} + \frac{218}{757}e^{8} - \frac{5486}{757}e^{7} - \frac{5072}{757}e^{6} + \frac{39600}{757}e^{5} + \frac{30874}{757}e^{4} - \frac{94705}{757}e^{3} - \frac{19291}{757}e^{2} + \frac{78735}{757}e - \frac{29048}{757}$ |
| 29 | $[29, 29, w^{2} - w - 1]$ | $-\frac{2903}{757}e^{9} - \frac{1432}{757}e^{8} + \frac{65872}{757}e^{7} + \frac{38741}{757}e^{6} - \frac{476724}{757}e^{5} - \frac{253191}{757}e^{4} + \frac{1163215}{757}e^{3} + \frac{113454}{757}e^{2} - \frac{948060}{757}e + \frac{327918}{757}$ |
| 31 | $[31, 31, w^{2} - 2]$ | $\phantom{-}\frac{681}{757}e^{9} + \frac{259}{757}e^{8} - \frac{15699}{757}e^{7} - \frac{7276}{757}e^{6} + \frac{116907}{757}e^{5} + \frac{46216}{757}e^{4} - \frac{303027}{757}e^{3} + \frac{4128}{757}e^{2} + \frac{261781}{757}e - \frac{102030}{757}$ |
| 37 | $[37, 37, 2w - 5]$ | $-\frac{2884}{757}e^{9} - \frac{1686}{757}e^{8} + \frac{65444}{757}e^{7} + \frac{43588}{757}e^{6} - \frac{472075}{757}e^{5} - \frac{279885}{757}e^{4} + \frac{1139994}{757}e^{3} + \frac{147244}{757}e^{2} - \frac{927775}{757}e + \frac{314440}{757}$ |
| 43 | $[43, 43, w^{2} - 2w - 5]$ | $\phantom{-}\frac{852}{757}e^{9} + \frac{244}{757}e^{8} - \frac{19551}{757}e^{7} - \frac{7559}{757}e^{6} + \frac{145122}{757}e^{5} + \frac{49724}{757}e^{4} - \frac{374999}{757}e^{3} + \frac{9223}{757}e^{2} + \frac{314142}{757}e - \frac{120380}{757}$ |
| 47 | $[47, 47, w^{2} - 3w - 2]$ | $-\frac{472}{757}e^{9} - \frac{25}{757}e^{8} + \frac{10991}{757}e^{7} + \frac{1547}{757}e^{6} - \frac{83936}{757}e^{5} - \frac{8284}{757}e^{4} + \frac{230033}{757}e^{3} - \frac{47274}{757}e^{2} - \frac{202158}{757}e + \frac{93060}{757}$ |
| 49 | $[49, 7, w^{2} + w - 4]$ | $-\frac{4293}{757}e^{9} - \frac{2253}{757}e^{8} + \frac{97582}{757}e^{7} + \frac{59537}{757}e^{6} - \frac{707588}{757}e^{5} - \frac{384375}{757}e^{4} + \frac{1731933}{757}e^{3} + \frac{174809}{757}e^{2} - \frac{1417409}{757}e + \frac{488332}{757}$ |
| 53 | $[53, 53, w^{2} - 2w - 6]$ | $\phantom{-}\frac{1151}{757}e^{9} + \frac{749}{757}e^{8} - \frac{26127}{757}e^{7} - \frac{18975}{757}e^{6} + \frac{188401}{757}e^{5} + \frac{122890}{757}e^{4} - \frac{454079}{757}e^{3} - \frac{89132}{757}e^{2} + \frac{365346}{757}e - \frac{109206}{757}$ |
| 71 | $[71, 71, w - 5]$ | $-\frac{4912}{757}e^{9} - \frac{2544}{757}e^{8} + \frac{111725}{757}e^{7} + \frac{67370}{757}e^{6} - \frac{811237}{757}e^{5} - \frac{434866}{757}e^{4} + \frac{1992295}{757}e^{3} + \frac{190382}{757}e^{2} - \frac{1637181}{757}e + \frac{568374}{757}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{2} + w + 4]$ | $-1$ |