Base field 4.4.2525.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[880,110,2w^{3} - 6w^{2} - 4w + 10]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $71$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} - 7x^{8} - 10x^{7} + 163x^{6} - 185x^{5} - 975x^{4} + 2169x^{3} + 255x^{2} - 2949x + 1194\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w]$ | $-1$ |
| 5 | $[5, 5, w^{3} - 2w^{2} - 2w + 3]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w^{2} + 4]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w^{2} - 2w - 3]$ | $\phantom{-}\frac{3071}{51963}e^{8} - \frac{9178}{51963}e^{7} - \frac{71204}{51963}e^{6} + \frac{72346}{17321}e^{5} + \frac{140742}{17321}e^{4} - \frac{473960}{17321}e^{3} - \frac{29393}{17321}e^{2} + \frac{553581}{17321}e - \frac{188490}{17321}$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}1$ |
| 29 | $[29, 29, w^{3} - 4w - 1]$ | $\phantom{-}\frac{1444}{51963}e^{8} - \frac{11033}{51963}e^{7} - \frac{23362}{51963}e^{6} + \frac{90267}{17321}e^{5} - \frac{8442}{17321}e^{4} - \frac{627722}{17321}e^{3} + \frac{434664}{17321}e^{2} + \frac{911247}{17321}e - \frac{464502}{17321}$ |
| 29 | $[29, 29, w^{3} - 3w^{2} - w + 4]$ | $-\frac{1838}{51963}e^{8} + \frac{12532}{51963}e^{7} + \frac{33191}{51963}e^{6} - \frac{101630}{17321}e^{5} - \frac{5520}{17321}e^{4} + \frac{685044}{17321}e^{3} - \frac{517278}{17321}e^{2} - \frac{854655}{17321}e + \frac{598296}{17321}$ |
| 41 | $[41, 41, w^{3} - 2w^{2} - w + 4]$ | $-\frac{8737}{103926}e^{8} + \frac{15763}{51963}e^{7} + \frac{101660}{51963}e^{6} - \frac{260021}{34642}e^{5} - \frac{191249}{17321}e^{4} + \frac{1815723}{34642}e^{3} - \frac{92625}{17321}e^{2} - \frac{2539771}{34642}e + \frac{430869}{17321}$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 2w + 2]$ | $\phantom{-}\frac{26159}{103926}e^{8} - \frac{55367}{51963}e^{7} - \frac{278218}{51963}e^{6} + \frac{899019}{34642}e^{5} + \frac{395747}{17321}e^{4} - \frac{6144753}{34642}e^{3} + \frac{1206966}{17321}e^{2} + \frac{8138323}{34642}e - \frac{1886496}{17321}$ |
| 59 | $[59, 59, -2w^{3} + 4w^{2} + 4w - 7]$ | $\phantom{-}\frac{4643}{103926}e^{8} - \frac{2292}{17321}e^{7} - \frac{51869}{51963}e^{6} + \frac{310229}{103926}e^{5} + \frac{92597}{17321}e^{4} - \frac{627667}{34642}e^{3} + \frac{52121}{17321}e^{2} + \frac{561665}{34642}e - \frac{214321}{17321}$ |
| 59 | $[59, 59, -3w^{2} + 2w + 7]$ | $-\frac{19013}{103926}e^{8} + \frac{13646}{17321}e^{7} + \frac{204602}{51963}e^{6} - \frac{2011697}{103926}e^{5} - \frac{297092}{17321}e^{4} + \frac{4638225}{34642}e^{3} - \frac{879989}{17321}e^{2} - \frac{6363657}{34642}e + \frac{1479619}{17321}$ |
| 61 | $[61, 61, -w^{3} + 4w^{2} - 6]$ | $-\frac{24433}{103926}e^{8} + \frac{51688}{51963}e^{7} + \frac{261305}{51963}e^{6} - \frac{842295}{34642}e^{5} - \frac{379321}{17321}e^{4} + \frac{5774593}{34642}e^{3} - \frac{1088350}{17321}e^{2} - \frac{7699375}{34642}e + \frac{1837780}{17321}$ |
| 61 | $[61, 61, w^{3} + w^{2} - 5w - 3]$ | $-\frac{3564}{17321}e^{8} + \frac{42349}{51963}e^{7} + \frac{235693}{51963}e^{6} - \frac{1044124}{51963}e^{5} - \frac{374931}{17321}e^{4} + \frac{2403488}{17321}e^{3} - \frac{739282}{17321}e^{2} - \frac{3170648}{17321}e + \frac{1377023}{17321}$ |
| 71 | $[71, 71, w^{3} + w^{2} - 4w - 6]$ | $\phantom{-}\frac{3071}{51963}e^{8} - \frac{9178}{51963}e^{7} - \frac{71204}{51963}e^{6} + \frac{72346}{17321}e^{5} + \frac{140742}{17321}e^{4} - \frac{473960}{17321}e^{3} - \frac{29393}{17321}e^{2} + \frac{605544}{17321}e - \frac{240453}{17321}$ |
| 71 | $[71, 71, 3w^{2} - 2w - 8]$ | $\phantom{-}\frac{1730}{51963}e^{8} - \frac{8780}{51963}e^{7} - \frac{13536}{17321}e^{6} + \frac{213337}{51963}e^{5} + \frac{78890}{17321}e^{4} - \frac{480383}{17321}e^{3} + \frac{18349}{17321}e^{2} + \frac{620200}{17321}e - \frac{97999}{17321}$ |
| 71 | $[71, 71, 3w^{2} - 4w - 7]$ | $-\frac{3617}{103926}e^{8} + \frac{2125}{17321}e^{7} + \frac{39467}{51963}e^{6} - \frac{332507}{103926}e^{5} - \frac{51382}{17321}e^{4} + \frac{787889}{34642}e^{3} - \frac{258707}{17321}e^{2} - \frac{906511}{34642}e + \frac{414409}{17321}$ |
| 71 | $[71, 71, w^{3} - 4w^{2} + w + 8]$ | $-\frac{4594}{51963}e^{8} + \frac{7438}{17321}e^{7} + \frac{98603}{51963}e^{6} - \frac{547912}{51963}e^{5} - \frac{132198}{17321}e^{4} + \frac{1247699}{17321}e^{3} - \frac{572801}{17321}e^{2} - \frac{1580355}{17321}e + \frac{971638}{17321}$ |
| 79 | $[79, 79, -2w^{3} + 3w^{2} + 5w - 2]$ | $-\frac{8134}{51963}e^{8} + \frac{11224}{17321}e^{7} + \frac{176891}{51963}e^{6} - \frac{815947}{51963}e^{5} - \frac{275404}{17321}e^{4} + \frac{1849417}{17321}e^{3} - \frac{596731}{17321}e^{2} - \frac{2444644}{17321}e + \frac{1196297}{17321}$ |
| 79 | $[79, 79, 2w^{2} - 3w - 7]$ | $-\frac{15718}{51963}e^{8} + \frac{62350}{51963}e^{7} + \frac{113090}{17321}e^{6} - \frac{1525223}{51963}e^{5} - \frac{508106}{17321}e^{4} + \frac{3482534}{17321}e^{3} - \frac{1281242}{17321}e^{2} - \frac{4545637}{17321}e + \frac{2202045}{17321}$ |
| 79 | $[79, 79, 2w^{2} - w - 8]$ | $-\frac{215}{34642}e^{8} - \frac{756}{17321}e^{7} + \frac{4726}{17321}e^{6} + \frac{31207}{34642}e^{5} - \frac{61413}{17321}e^{4} - \frac{201409}{34642}e^{3} + \frac{276644}{17321}e^{2} + \frac{530593}{34642}e - \frac{341843}{17321}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,-w^{3} + w^{2} + 3w]$ | $1$ |
| $11$ | $[11,11,w^{2} - 4]$ | $-1$ |
| $16$ | $[16,2,2]$ | $-1$ |