Base field 5.5.176281.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 3x^{2} + 4x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[11, 11, -w^{2} + 3]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} + 7x^{8} + 3x^{7} - 61x^{6} - 83x^{5} + 120x^{4} + 217x^{3} + 19x^{2} - 35x - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - w - 2]$ | $\phantom{-}\frac{151}{365}e^{8} + \frac{176}{73}e^{7} - \frac{477}{365}e^{6} - \frac{8137}{365}e^{5} - \frac{3679}{365}e^{4} + \frac{17453}{365}e^{3} + \frac{12976}{365}e^{2} - \frac{1268}{365}e - \frac{1599}{365}$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}\frac{78}{365}e^{8} + \frac{103}{73}e^{7} + \frac{34}{365}e^{6} - \frac{4706}{365}e^{5} - \frac{4482}{365}e^{4} + \frac{10664}{365}e^{3} + \frac{11808}{365}e^{2} - \frac{2874}{365}e - \frac{1307}{365}$ |
| 11 | $[11, 11, -w^{2} + 3]$ | $-1$ |
| 13 | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $-\frac{208}{365}e^{8} - \frac{226}{73}e^{7} + \frac{1126}{365}e^{6} + \frac{10846}{365}e^{5} + \frac{637}{365}e^{4} - \frac{24909}{365}e^{3} - \frac{8493}{365}e^{2} + \frac{5474}{365}e + \frac{1417}{365}$ |
| 23 | $[23, 23, -w^{4} + 5w^{2} + w - 4]$ | $\phantom{-}\frac{26}{365}e^{8} + \frac{10}{73}e^{7} - \frac{597}{365}e^{6} - \frac{717}{365}e^{5} + \frac{3981}{365}e^{4} + \frac{1243}{365}e^{3} - \frac{6649}{365}e^{2} + \frac{1597}{365}e + \frac{51}{365}$ |
| 31 | $[31, 31, -w^{4} + w^{3} + 5w^{2} - 2w - 2]$ | $\phantom{-}\frac{83}{365}e^{8} + \frac{60}{73}e^{7} - \frac{1246}{365}e^{6} - \frac{3426}{365}e^{5} + \frac{7388}{365}e^{4} + \frac{9794}{365}e^{3} - \frac{13322}{365}e^{2} - \frac{6989}{365}e + \frac{598}{365}$ |
| 32 | $[32, 2, 2]$ | $-\frac{208}{365}e^{8} - \frac{226}{73}e^{7} + \frac{1126}{365}e^{6} + \frac{10846}{365}e^{5} + \frac{637}{365}e^{4} - \frac{24909}{365}e^{3} - \frac{8128}{365}e^{2} + \frac{6569}{365}e + \frac{687}{365}$ |
| 37 | $[37, 37, w^{3} - 3w - 1]$ | $-\frac{161}{365}e^{8} - \frac{163}{73}e^{7} + \frac{1212}{365}e^{6} + \frac{8132}{365}e^{5} - \frac{2906}{365}e^{4} - \frac{20093}{365}e^{3} + \frac{2609}{365}e^{2} + \frac{7308}{365}e - \frac{2576}{365}$ |
| 41 | $[41, 41, w^{4} - w^{3} - 3w^{2} + w + 1]$ | $-\frac{442}{365}e^{8} - \frac{462}{73}e^{7} + \frac{2849}{365}e^{6} + \frac{22409}{365}e^{5} - \frac{3072}{365}e^{4} - \frac{51791}{365}e^{3} - \frac{6687}{365}e^{2} + \frac{12271}{365}e - \frac{867}{365}$ |
| 47 | $[47, 47, -w^{3} + w^{2} + 4w]$ | $-\frac{83}{365}e^{8} - \frac{60}{73}e^{7} + \frac{1246}{365}e^{6} + \frac{3426}{365}e^{5} - \frac{7023}{365}e^{4} - \frac{8334}{365}e^{3} + \frac{12227}{365}e^{2} + \frac{784}{365}e - \frac{3153}{365}$ |
| 61 | $[61, 61, -w^{4} + 6w^{2} + w - 4]$ | $\phantom{-}\frac{99}{365}e^{8} + \frac{83}{73}e^{7} - \frac{1108}{365}e^{6} - \frac{4148}{365}e^{5} + \frac{4784}{365}e^{4} + \frac{7667}{365}e^{3} - \frac{6576}{365}e^{2} + \frac{5393}{365}e + \frac{2314}{365}$ |
| 67 | $[67, 67, -w^{4} + w^{3} + 5w^{2} - 4w - 3]$ | $-\frac{187}{365}e^{8} - \frac{173}{73}e^{7} + \frac{1809}{365}e^{6} + \frac{8849}{365}e^{5} - \frac{6887}{365}e^{4} - \frac{21336}{365}e^{3} + \frac{9258}{365}e^{2} + \frac{6806}{365}e - \frac{2627}{365}$ |
| 71 | $[71, 71, w^{4} - 6w^{2} + 7]$ | $\phantom{-}\frac{22}{365}e^{8} - \frac{14}{73}e^{7} - \frac{1179}{365}e^{6} - \frac{354}{365}e^{5} + \frac{9742}{365}e^{4} + \frac{5516}{365}e^{3} - \frac{19833}{365}e^{2} - \frac{13361}{365}e + \frac{1812}{365}$ |
| 73 | $[73, 73, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ | $-\frac{236}{365}e^{8} - \frac{321}{73}e^{7} - \frac{393}{365}e^{6} + \frac{14482}{365}e^{5} + \frac{16874}{365}e^{4} - \frac{31498}{365}e^{3} - \frac{44936}{365}e^{2} + \frac{4428}{365}e + \frac{4984}{365}$ |
| 83 | $[83, 83, -w^{4} + 2w^{3} + 4w^{2} - 6w - 2]$ | $\phantom{-}\frac{31}{365}e^{8} + \frac{40}{73}e^{7} - \frac{52}{365}e^{6} - \frac{1992}{365}e^{5} - \frac{1304}{365}e^{4} + \frac{5118}{365}e^{3} + \frac{4356}{365}e^{2} - \frac{2153}{365}e - \frac{2424}{365}$ |
| 83 | $[83, 83, -w^{4} + 5w^{2} + 2w - 4]$ | $-\frac{92}{73}e^{8} - \frac{497}{73}e^{7} + \frac{484}{73}e^{6} + \frac{4626}{73}e^{5} + \frac{300}{73}e^{4} - \frac{9615}{73}e^{3} - \frac{3567}{73}e^{2} - \frac{204}{73}e + \frac{426}{73}$ |
| 83 | $[83, 83, w^{4} - 5w^{2} + 2]$ | $\phantom{-}\frac{19}{365}e^{8} - \frac{32}{73}e^{7} - \frac{1433}{365}e^{6} + \frac{922}{365}e^{5} + \frac{13059}{365}e^{4} - \frac{678}{365}e^{3} - \frac{29356}{365}e^{2} - \frac{6147}{365}e + \frac{5049}{365}$ |
| 89 | $[89, 89, -2w^{4} + 2w^{3} + 9w^{2} - 6w - 4]$ | $-\frac{231}{365}e^{8} - \frac{291}{73}e^{7} + \frac{152}{365}e^{6} + \frac{13207}{365}e^{5} + \frac{11589}{365}e^{4} - \frac{27623}{365}e^{3} - \frac{34661}{365}e^{2} - \frac{417}{365}e + \frac{5064}{365}$ |
| 101 | $[101, 101, -2w^{4} + 2w^{3} + 8w^{2} - 3w - 3]$ | $\phantom{-}\frac{83}{365}e^{8} + \frac{60}{73}e^{7} - \frac{1246}{365}e^{6} - \frac{3426}{365}e^{5} + \frac{7023}{365}e^{4} + \frac{8334}{365}e^{3} - \frac{11497}{365}e^{2} + \frac{311}{365}e - \frac{1227}{365}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -w^{2} + 3]$ | $1$ |