Base field 6.6.1081856.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - 2x^{3} + 7x^{2} + 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[31, 31, -w^{3} + 4w + 1]$ |
| 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:
| \(x^{10} - 9x^{9} - 5x^{8} + 233x^{7} - 392x^{6} - 1420x^{5} + 3168x^{4} + 2736x^{3} - 6608x^{2} - 576x + 2688\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{4} - w^{3} - 4w^{2} + w + 1]$ | $\phantom{-}e$ |
| 8 | $[8, 2, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 5w]$ | $-\frac{11}{33016}e^{9} - \frac{217}{33016}e^{8} + \frac{425}{8254}e^{7} + \frac{4253}{33016}e^{6} - \frac{36715}{33016}e^{5} - \frac{450}{4127}e^{4} + \frac{94071}{16508}e^{3} - \frac{4614}{4127}e^{2} - \frac{33418}{4127}e + \frac{2375}{4127}$ |
| 17 | $[17, 17, -w^{2} + w + 2]$ | $-\frac{249}{66032}e^{9} + \frac{733}{33016}e^{8} + \frac{5841}{66032}e^{7} - \frac{5365}{8254}e^{6} - \frac{12039}{33016}e^{5} + \frac{44215}{8254}e^{4} - \frac{623}{4127}e^{3} - \frac{66479}{4127}e^{2} + \frac{9707}{4127}e + \frac{49204}{4127}$ |
| 23 | $[23, 23, -w^{4} + 2w^{3} + 3w^{2} - 4w - 1]$ | $\phantom{-}\frac{71}{33016}e^{9} + \frac{175}{66032}e^{8} - \frac{6563}{66032}e^{7} - \frac{8755}{66032}e^{6} + \frac{99901}{66032}e^{5} + \frac{36005}{16508}e^{4} - \frac{67791}{8254}e^{3} - \frac{51258}{4127}e^{2} + \frac{42364}{4127}e + \frac{51828}{4127}$ |
| 25 | $[25, 5, -w^{3} + w^{2} + 4w]$ | $-\frac{29}{8254}e^{9} + \frac{1051}{66032}e^{8} + \frac{365}{4127}e^{7} - \frac{29233}{66032}e^{6} - \frac{10869}{33016}e^{5} + \frac{25401}{8254}e^{4} - \frac{46857}{16508}e^{3} - \frac{40661}{8254}e^{2} + \frac{52038}{4127}e + \frac{5536}{4127}$ |
| 31 | $[31, 31, -w^{3} + 4w + 1]$ | $-1$ |
| 31 | $[31, 31, w^{5} - 6w^{3} - w^{2} + 5w]$ | $\phantom{-}\frac{63}{8254}e^{9} - \frac{891}{16508}e^{8} - \frac{9983}{66032}e^{7} + \frac{25945}{16508}e^{6} - \frac{2727}{66032}e^{5} - \frac{418395}{33016}e^{4} + \frac{46129}{8254}e^{3} + \frac{295821}{8254}e^{2} - \frac{43316}{4127}e - \frac{85174}{4127}$ |
| 41 | $[41, 41, -w^{5} + w^{4} + 5w^{3} - 2w^{2} - 6w - 1]$ | $\phantom{-}\frac{27}{4127}e^{9} - \frac{2117}{33016}e^{8} - \frac{741}{33016}e^{7} + \frac{55679}{33016}e^{6} - \frac{86067}{33016}e^{5} - \frac{45565}{4127}e^{4} + \frac{278943}{16508}e^{3} + \frac{234105}{8254}e^{2} - \frac{82525}{4127}e - \frac{70648}{4127}$ |
| 47 | $[47, 47, -w^{5} + w^{4} + 6w^{3} - 4w^{2} - 8w + 2]$ | $\phantom{-}\frac{193}{66032}e^{9} - \frac{535}{33016}e^{8} - \frac{3283}{33016}e^{7} + \frac{2535}{4127}e^{6} + \frac{57397}{66032}e^{5} - \frac{232171}{33016}e^{4} - \frac{4549}{16508}e^{3} + \frac{93378}{4127}e^{2} - \frac{16358}{4127}e - \frac{21398}{4127}$ |
| 49 | $[49, 7, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 3]$ | $-\frac{169}{66032}e^{9} + \frac{2669}{66032}e^{8} - \frac{1573}{33016}e^{7} - \frac{71975}{66032}e^{6} + \frac{160025}{66032}e^{5} + \frac{62495}{8254}e^{4} - \frac{114131}{8254}e^{3} - \frac{87219}{4127}e^{2} + \frac{52814}{4127}e + \frac{74334}{4127}$ |
| 71 | $[71, 71, -w^{4} + 5w^{2} + w - 3]$ | $-\frac{79}{8254}e^{9} + \frac{1645}{33016}e^{8} + \frac{17759}{66032}e^{7} - \frac{49281}{33016}e^{6} - \frac{133361}{66032}e^{5} + \frac{416959}{33016}e^{4} + \frac{43693}{8254}e^{3} - \frac{295485}{8254}e^{2} - \frac{10798}{4127}e + \frac{102744}{4127}$ |
| 71 | $[71, 71, w^{4} - 5w^{2} - 2w + 4]$ | $-\frac{383}{66032}e^{9} + \frac{114}{4127}e^{8} + \frac{5959}{33016}e^{7} - \frac{27821}{33016}e^{6} - \frac{109283}{66032}e^{5} + \frac{231845}{33016}e^{4} + \frac{94005}{16508}e^{3} - \frac{62692}{4127}e^{2} - \frac{32886}{4127}e + \frac{12270}{4127}$ |
| 73 | $[73, 73, -2w^{5} + w^{4} + 10w^{3} - 9w - 1]$ | $-\frac{445}{66032}e^{9} + \frac{713}{16508}e^{8} + \frac{4747}{33016}e^{7} - \frac{21049}{16508}e^{6} - \frac{8573}{66032}e^{5} + \frac{43048}{4127}e^{4} - \frac{95231}{16508}e^{3} - \frac{110587}{4127}e^{2} + \frac{71032}{4127}e + \frac{26842}{4127}$ |
| 73 | $[73, 73, -w^{5} + 6w^{3} + 2w^{2} - 5w - 1]$ | $\phantom{-}\frac{693}{66032}e^{9} - \frac{2837}{66032}e^{8} - \frac{20433}{66032}e^{7} + \frac{78729}{66032}e^{6} + \frac{42783}{16508}e^{5} - \frac{137269}{16508}e^{4} - \frac{31481}{4127}e^{3} + \frac{58674}{4127}e^{2} - \frac{7972}{4127}e - \frac{2590}{4127}$ |
| 79 | $[79, 79, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 3]$ | $\phantom{-}\frac{345}{33016}e^{9} - \frac{831}{8254}e^{8} - \frac{2711}{66032}e^{7} + \frac{86467}{33016}e^{6} - \frac{271841}{66032}e^{5} - \frac{67676}{4127}e^{4} + \frac{465997}{16508}e^{3} + \frac{149214}{4127}e^{2} - \frac{148720}{4127}e - \frac{71112}{4127}$ |
| 89 | $[89, 89, w^{5} - 7w^{3} - w^{2} + 9w]$ | $\phantom{-}\frac{1531}{66032}e^{9} - \frac{4971}{33016}e^{8} - \frac{3501}{8254}e^{7} + \frac{16303}{4127}e^{6} - \frac{35183}{66032}e^{5} - \frac{825119}{33016}e^{4} + \frac{49211}{4127}e^{3} + \frac{425705}{8254}e^{2} - \frac{59817}{4127}e - \frac{82926}{4127}$ |
| 97 | $[97, 97, 2w^{5} - 2w^{4} - 10w^{3} + 5w^{2} + 10w - 1]$ | $\phantom{-}\frac{747}{33016}e^{9} - \frac{2199}{16508}e^{8} - \frac{30919}{66032}e^{7} + \frac{116379}{33016}e^{6} + \frac{49547}{66032}e^{5} - \frac{377881}{16508}e^{4} + \frac{101619}{16508}e^{3} + \frac{204905}{4127}e^{2} - \frac{41734}{4127}e - \frac{72366}{4127}$ |
| 103 | $[103, 103, w^{5} - w^{4} - 4w^{3} + w^{2} + 3w + 2]$ | $-\frac{1405}{66032}e^{9} + \frac{9051}{66032}e^{8} + \frac{1659}{4127}e^{7} - \frac{243157}{66032}e^{6} + \frac{27279}{66032}e^{5} + \frac{102575}{4127}e^{4} - \frac{241875}{16508}e^{3} - \frac{237264}{4127}e^{2} + \frac{123274}{4127}e + \frac{129728}{4127}$ |
| 103 | $[103, 103, -2w^{5} + w^{4} + 11w^{3} - w^{2} - 11w - 1]$ | $\phantom{-}\frac{101}{16508}e^{9} + \frac{91}{66032}e^{8} - \frac{1276}{4127}e^{7} + \frac{7003}{66032}e^{6} + \frac{152343}{33016}e^{5} - \frac{42357}{16508}e^{4} - \frac{81264}{4127}e^{3} + \frac{10819}{4127}e^{2} + \frac{77166}{4127}e + \frac{46430}{4127}$ |
| 103 | $[103, 103, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ | $\phantom{-}\frac{521}{66032}e^{9} - \frac{3979}{66032}e^{8} - \frac{5857}{66032}e^{7} + \frac{100959}{66032}e^{6} - \frac{23827}{16508}e^{5} - \frac{38492}{4127}e^{4} + \frac{71407}{8254}e^{3} + \frac{107392}{4127}e^{2} - \frac{13366}{4127}e - \frac{104080}{4127}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31, 31, -w^{3} + 4w + 1]$ | $1$ |