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: | $9$ |
| 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:
| \(x^{9} - 35x^{7} - 7x^{6} + 394x^{5} + 136x^{4} - 1582x^{3} - 820x^{2} + 1608x + 720\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w + 1]$ | $\phantom{-}\frac{2189}{1455528}e^{8} - \frac{651}{121294}e^{7} - \frac{71011}{1455528}e^{6} + \frac{226129}{1455528}e^{5} + \frac{375325}{727764}e^{4} - \frac{560137}{363882}e^{3} - \frac{1209763}{727764}e^{2} + \frac{1891453}{363882}e + \frac{35962}{60647}$ |
| 11 | $[11, 11, w^{2} - w - 2]$ | $\phantom{-}\frac{2189}{363882}e^{8} - \frac{1302}{60647}e^{7} - \frac{71011}{363882}e^{6} + \frac{226129}{363882}e^{5} + \frac{375325}{181941}e^{4} - \frac{938333}{181941}e^{3} - \frac{1391704}{181941}e^{2} + \frac{1781555}{181941}e + \frac{507730}{60647}$ |
| 17 | $[17, 17, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 3w - 3]$ | $-1$ |
| 27 | $[27, 3, w^{5} - w^{4} - 5w^{3} + w^{2} + 6w + 1]$ | $\phantom{-}\frac{1397}{2183292}e^{8} - \frac{12107}{363882}e^{7} - \frac{59947}{2183292}e^{6} + \frac{1843039}{2183292}e^{5} + \frac{435647}{545823}e^{4} - \frac{2926591}{545823}e^{3} - \frac{7120795}{1091646}e^{2} + \frac{3227659}{545823}e + \frac{1371602}{181941}$ |
| 27 | $[27, 3, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $-\frac{34697}{4366584}e^{8} + \frac{7145}{727764}e^{7} + \frac{1451383}{4366584}e^{6} - \frac{1524835}{4366584}e^{5} - \frac{2375191}{545823}e^{4} + \frac{1665053}{545823}e^{3} + \frac{40101115}{2183292}e^{2} - \frac{1690910}{545823}e - \frac{2134513}{181941}$ |
| 37 | $[37, 37, -w^{2} + 2w + 2]$ | $\phantom{-}\frac{34693}{2183292}e^{8} - \frac{8960}{181941}e^{7} - \frac{1105823}{2183292}e^{6} + \frac{2869073}{2183292}e^{5} + \frac{5560295}{1091646}e^{4} - \frac{5159630}{545823}e^{3} - \frac{17706281}{1091646}e^{2} + \frac{6650642}{545823}e + \frac{1520746}{181941}$ |
| 47 | $[47, 47, -w^{5} + 2w^{4} + 3w^{3} - 3w^{2} - 2w - 1]$ | $\phantom{-}\frac{13343}{727764}e^{8} - \frac{5803}{121294}e^{7} - \frac{469417}{727764}e^{6} + \frac{1076653}{727764}e^{5} + \frac{1251320}{181941}e^{4} - \frac{2377513}{181941}e^{3} - \frac{7598995}{363882}e^{2} + \frac{4754521}{181941}e + \frac{659666}{60647}$ |
| 53 | $[53, 53, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} + 3]$ | $-\frac{22609}{1455528}e^{8} + \frac{439}{60647}e^{7} + \frac{782639}{1455528}e^{6} - \frac{341777}{1455528}e^{5} - \frac{4165607}{727764}e^{4} + \frac{963293}{363882}e^{3} + \frac{14398679}{727764}e^{2} - \frac{2547545}{363882}e - \frac{831230}{60647}$ |
| 59 | $[59, 59, w^{4} - 2w^{3} - 2w^{2} + 3w - 2]$ | $\phantom{-}\frac{46571}{1455528}e^{8} - \frac{6425}{121294}e^{7} - \frac{1462885}{1455528}e^{6} + \frac{2030167}{1455528}e^{5} + \frac{6976015}{727764}e^{4} - \frac{3872785}{363882}e^{3} - \frac{19912285}{727764}e^{2} + \frac{6072181}{363882}e + \frac{878296}{60647}$ |
| 64 | $[64, 2, -2]$ | $-\frac{12877}{4366584}e^{8} + \frac{17827}{727764}e^{7} + \frac{602579}{4366584}e^{6} - \frac{3940235}{4366584}e^{5} - \frac{1919851}{1091646}e^{4} + \frac{5052835}{545823}e^{3} + \frac{12911063}{2183292}e^{2} - \frac{11754847}{545823}e - \frac{896426}{181941}$ |
| 67 | $[67, 67, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w - 2]$ | $\phantom{-}\frac{14689}{545823}e^{8} - \frac{14695}{363882}e^{7} - \frac{490058}{545823}e^{6} + \frac{1182079}{1091646}e^{5} + \frac{10119743}{1091646}e^{4} - \frac{4629776}{545823}e^{3} - \frac{16384360}{545823}e^{2} + \frac{7964474}{545823}e + \frac{3690778}{181941}$ |
| 67 | $[67, 67, -w^{5} + 3w^{4} + w^{3} - 7w^{2} + 3w + 2]$ | $\phantom{-}\frac{63907}{2183292}e^{8} - \frac{6095}{181941}e^{7} - \frac{2109377}{2183292}e^{6} + \frac{1853495}{2183292}e^{5} + \frac{10897457}{1091646}e^{4} - \frac{3340667}{545823}e^{3} - \frac{36160025}{1091646}e^{2} + \frac{2740601}{545823}e + \frac{2580370}{181941}$ |
| 71 | $[71, 71, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $\phantom{-}\frac{118}{181941}e^{8} - \frac{2137}{121294}e^{7} - \frac{5324}{181941}e^{6} + \frac{198175}{363882}e^{5} + \frac{116087}{363882}e^{4} - \frac{807899}{181941}e^{3} + \frac{142277}{181941}e^{2} + \frac{903629}{181941}e - \frac{649586}{60647}$ |
| 71 | $[71, 71, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $-\frac{2189}{181941}e^{8} + \frac{2604}{60647}e^{7} + \frac{71011}{181941}e^{6} - \frac{226129}{181941}e^{5} - \frac{750650}{181941}e^{4} + \frac{1876666}{181941}e^{3} + \frac{2601467}{181941}e^{2} - \frac{3563110}{181941}e - \frac{287696}{60647}$ |
| 73 | $[73, 73, 2w^{5} - 4w^{4} - 7w^{3} + 10w^{2} + 5w - 3]$ | $\phantom{-}\frac{41113}{2183292}e^{8} - \frac{4220}{181941}e^{7} - \frac{1173455}{2183292}e^{6} + \frac{1367933}{2183292}e^{5} + \frac{4470293}{1091646}e^{4} - \frac{3118058}{545823}e^{3} - \frac{5870549}{1091646}e^{2} + \frac{7187831}{545823}e + \frac{77014}{181941}$ |
| 83 | $[83, 83, w^{4} - 2w^{3} - 4w^{2} + 5w + 2]$ | $-\frac{4169}{1455528}e^{8} + \frac{4613}{242588}e^{7} + \frac{98671}{1455528}e^{6} - \frac{732379}{1455528}e^{5} - \frac{124990}{181941}e^{4} + \frac{778880}{181941}e^{3} + \frac{3170755}{727764}e^{2} - \frac{2368466}{181941}e - \frac{321745}{60647}$ |
| 83 | $[83, 83, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 3]$ | $\phantom{-}\frac{10737}{485176}e^{8} - \frac{1157}{121294}e^{7} - \frac{337447}{485176}e^{6} + \frac{195325}{485176}e^{5} + \frac{1473921}{242588}e^{4} - \frac{658145}{121294}e^{3} - \frac{3028791}{242588}e^{2} + \frac{1740299}{121294}e + \frac{136206}{60647}$ |
| 89 | $[89, 89, -w^{5} + w^{4} + 6w^{3} - 2w^{2} - 8w + 1]$ | $\phantom{-}\frac{11981}{727764}e^{8} - \frac{5547}{121294}e^{7} - \frac{340123}{727764}e^{6} + \frac{844195}{727764}e^{5} + \frac{702602}{181941}e^{4} - \frac{1454746}{181941}e^{3} - \frac{2756803}{363882}e^{2} + \frac{1398436}{181941}e - \frac{316816}{60647}$ |
| 97 | $[97, 97, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 7w]$ | $\phantom{-}\frac{5233}{545823}e^{8} - \frac{16135}{363882}e^{7} - \frac{137426}{545823}e^{6} + \frac{1176331}{1091646}e^{5} + \frac{2556275}{1091646}e^{4} - \frac{4202912}{545823}e^{3} - \frac{5259049}{545823}e^{2} + \frac{10172108}{545823}e + \frac{1496482}{181941}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 3w - 3]$ | $1$ |