Base field 6.6.1767625.1
Generator \(w\), with minimal polynomial \(x^{6} - 7x^{4} - x^{3} + 11x^{2} + x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[16, 2, -\frac{1}{2}w^{5} + \frac{1}{2}w^{4} + 3w^{3} - \frac{5}{2}w^{2} - 3w + \frac{5}{2}]$ |
| 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:
| \(x^{10} + 9x^{9} + 15x^{8} - 73x^{7} - 234x^{6} + 71x^{5} + 776x^{4} + 402x^{3} - 563x^{2} - 271x + 161\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w + 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -\frac{1}{2}w^{5} + \frac{1}{2}w^{4} + 3w^{3} - \frac{3}{2}w^{2} - 5w + \frac{1}{2}]$ | $-\frac{98}{279}e^{9} - \frac{733}{279}e^{8} - \frac{347}{279}e^{7} + \frac{7804}{279}e^{6} + \frac{11471}{279}e^{5} - \frac{8335}{93}e^{4} - \frac{42070}{279}e^{3} + \frac{23611}{279}e^{2} + \frac{9647}{93}e - \frac{13336}{279}$ |
| 11 | $[11, 11, \frac{1}{2}w^{5} + \frac{1}{2}w^{4} - 4w^{3} - \frac{5}{2}w^{2} + 6w + \frac{1}{2}]$ | $\phantom{-}\frac{191}{279}e^{9} + \frac{1477}{279}e^{8} + \frac{998}{279}e^{7} - \frac{15244}{279}e^{6} - \frac{25793}{279}e^{5} + \frac{15217}{93}e^{4} + \frac{92197}{279}e^{3} - \frac{36073}{279}e^{2} - \frac{20528}{93}e + \frac{24124}{279}$ |
| 16 | $[16, 2, -\frac{1}{2}w^{5} + \frac{1}{2}w^{4} + 3w^{3} - \frac{5}{2}w^{2} - 3w + \frac{5}{2}]$ | $\phantom{-}1$ |
| 29 | $[29, 29, -\frac{1}{2}w^{5} - \frac{1}{2}w^{4} + 4w^{3} + \frac{5}{2}w^{2} - 6w + \frac{1}{2}]$ | $\phantom{-}\frac{47}{279}e^{9} + \frac{343}{279}e^{8} + \frac{44}{279}e^{7} - \frac{4147}{279}e^{6} - \frac{4895}{279}e^{5} + \frac{5344}{93}e^{4} + \frac{20854}{279}e^{3} - \frac{21826}{279}e^{2} - \frac{5810}{93}e + \frac{11452}{279}$ |
| 41 | $[41, 41, \frac{1}{2}w^{5} - \frac{1}{2}w^{4} - 3w^{3} + \frac{3}{2}w^{2} + 3w + \frac{3}{2}]$ | $-\frac{335}{279}e^{9} - \frac{2611}{279}e^{8} - \frac{1952}{279}e^{7} + \frac{26341}{279}e^{6} + \frac{46691}{279}e^{5} - \frac{25090}{93}e^{4} - \frac{163540}{279}e^{3} + \frac{50320}{279}e^{2} + \frac{35246}{93}e - \frac{37354}{279}$ |
| 41 | $[41, 41, \frac{1}{2}w^{5} - \frac{1}{2}w^{4} - 2w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}]$ | $\phantom{-}\frac{395}{279}e^{9} + \frac{3037}{279}e^{8} + \frac{1931}{279}e^{7} - \frac{31546}{279}e^{6} - \frac{51818}{279}e^{5} + \frac{32017}{93}e^{4} + \frac{186268}{279}e^{3} - \frac{79483}{279}e^{2} - \frac{42386}{93}e + \frac{50353}{279}$ |
| 59 | $[59, 59, -\frac{3}{2}w^{5} + \frac{1}{2}w^{4} + 9w^{3} + \frac{1}{2}w^{2} - 11w - \frac{5}{2}]$ | $-\frac{13}{9}e^{9} - \frac{101}{9}e^{8} - \frac{70}{9}e^{7} + \frac{1040}{9}e^{6} + \frac{1762}{9}e^{5} - \frac{1049}{3}e^{4} - \frac{6284}{9}e^{3} + \frac{2648}{9}e^{2} + \frac{1435}{3}e - \frac{1736}{9}$ |
| 59 | $[59, 59, -\frac{1}{2}w^{5} - \frac{1}{2}w^{4} + 3w^{3} + \frac{5}{2}w^{2} - 4w - \frac{1}{2}]$ | $\phantom{-}\frac{8}{31}e^{9} + \frac{63}{31}e^{8} + \frac{53}{31}e^{7} - \frac{601}{31}e^{6} - \frac{1068}{31}e^{5} + \frac{1661}{31}e^{4} + \frac{3359}{31}e^{3} - \frac{1241}{31}e^{2} - \frac{1740}{31}e + \frac{828}{31}$ |
| 59 | $[59, 59, -\frac{1}{2}w^{5} + \frac{1}{2}w^{4} + 2w^{3} - \frac{1}{2}w^{2} - \frac{3}{2}]$ | $\phantom{-}\frac{41}{31}e^{9} + \frac{319}{31}e^{8} + \frac{229}{31}e^{7} - \frac{3239}{31}e^{6} - \frac{5520}{31}e^{5} + \frac{9741}{31}e^{4} + \frac{19412}{31}e^{3} - \frac{8565}{31}e^{2} - \frac{13366}{31}e + \frac{5778}{31}$ |
| 59 | $[59, 59, \frac{3}{2}w^{5} - \frac{1}{2}w^{4} - 9w^{3} + \frac{1}{2}w^{2} + 11w - \frac{1}{2}]$ | $-\frac{263}{279}e^{9} - \frac{2044}{279}e^{8} - \frac{1475}{279}e^{7} + \frac{20653}{279}e^{6} + \frac{35684}{279}e^{5} - \frac{19921}{93}e^{4} - \frac{124660}{279}e^{3} + \frac{42220}{279}e^{2} + \frac{27050}{93}e - \frac{28786}{279}$ |
| 61 | $[61, 61, \frac{1}{2}w^{5} - \frac{1}{2}w^{4} - 3w^{3} + \frac{1}{2}w^{2} + 4w + \frac{5}{2}]$ | $\phantom{-}\frac{85}{279}e^{9} + \frac{650}{279}e^{8} + \frac{412}{279}e^{7} - \frac{6746}{279}e^{6} - \frac{11239}{279}e^{5} + \frac{6752}{93}e^{4} + \frac{40475}{279}e^{3} - \frac{15437}{279}e^{2} - \frac{8782}{93}e + \frac{8162}{279}$ |
| 71 | $[71, 71, -\frac{1}{2}w^{5} - \frac{1}{2}w^{4} + 5w^{3} + \frac{5}{2}w^{2} - 11w - \frac{3}{2}]$ | $\phantom{-}\frac{82}{93}e^{9} + \frac{638}{93}e^{8} + \frac{427}{93}e^{7} - \frac{6695}{93}e^{6} - \frac{11257}{93}e^{5} + \frac{6897}{31}e^{4} + \frac{40994}{93}e^{3} - \frac{18122}{93}e^{2} - \frac{9634}{31}e + \frac{12176}{93}$ |
| 71 | $[71, 71, -\frac{1}{2}w^{5} + \frac{1}{2}w^{4} + 4w^{3} - \frac{5}{2}w^{2} - 7w + \frac{3}{2}]$ | $-\frac{212}{279}e^{9} - \frac{1654}{279}e^{8} - \frac{1172}{279}e^{7} + \frac{16996}{279}e^{6} + \frac{29108}{279}e^{5} - \frac{16837}{93}e^{4} - \frac{102607}{279}e^{3} + \frac{39040}{279}e^{2} + \frac{22097}{93}e - \frac{28297}{279}$ |
| 79 | $[79, 79, -w^{5} + 6w^{3} + 2w^{2} - 8w - 2]$ | $\phantom{-}\frac{488}{279}e^{9} + \frac{3781}{279}e^{8} + \frac{2582}{279}e^{7} - \frac{38707}{279}e^{6} - \frac{64466}{279}e^{5} + \frac{39178}{93}e^{4} + \frac{227746}{279}e^{3} - \frac{102547}{279}e^{2} - \frac{52616}{93}e + \frac{65047}{279}$ |
| 79 | $[79, 79, -\frac{3}{2}w^{5} + \frac{3}{2}w^{4} + 9w^{3} - \frac{11}{2}w^{2} - 12w + \frac{3}{2}]$ | $-\frac{220}{279}e^{9} - \frac{1748}{279}e^{8} - \frac{1411}{279}e^{7} + \frac{17690}{279}e^{6} + \frac{31912}{279}e^{5} - \frac{17339}{93}e^{4} - \frac{111422}{279}e^{3} + \frac{41366}{279}e^{2} + \frac{24847}{93}e - \frac{30923}{279}$ |
| 81 | $[81, 3, \frac{1}{2}w^{5} + \frac{1}{2}w^{4} - 4w^{3} - \frac{5}{2}w^{2} + 8w + \frac{3}{2}]$ | $\phantom{-}\frac{322}{279}e^{9} + \frac{2528}{279}e^{8} + \frac{2017}{279}e^{7} - \frac{25004}{279}e^{6} - \frac{45064}{279}e^{5} + \frac{23321}{93}e^{4} + \frac{153575}{279}e^{3} - \frac{45215}{279}e^{2} - \frac{32056}{93}e + \frac{31622}{279}$ |
| 89 | $[89, 89, \frac{3}{2}w^{5} - \frac{1}{2}w^{4} - 10w^{3} - \frac{1}{2}w^{2} + 14w + \frac{7}{2}]$ | $-\frac{509}{279}e^{9} - \frac{3958}{279}e^{8} - \frac{2756}{279}e^{7} + \frac{40738}{279}e^{6} + \frac{69455}{279}e^{5} - \frac{40426}{93}e^{4} - \frac{246247}{279}e^{3} + \frac{92680}{279}e^{2} + \frac{54185}{93}e - \frac{61408}{279}$ |
| 89 | $[89, 89, \frac{3}{2}w^{5} - \frac{1}{2}w^{4} - 9w^{3} + \frac{1}{2}w^{2} + 10w - \frac{1}{2}]$ | $-\frac{289}{279}e^{9} - \frac{2210}{279}e^{8} - \frac{1345}{279}e^{7} + \frac{23048}{279}e^{6} + \frac{36985}{279}e^{5} - \frac{24017}{93}e^{4} - \frac{133988}{279}e^{3} + \frac{67775}{279}e^{2} + \frac{32128}{93}e - \frac{42761}{279}$ |
| 89 | $[89, 89, \frac{3}{2}w^{5} - \frac{1}{2}w^{4} - 10w^{3} - \frac{1}{2}w^{2} + 15w + \frac{9}{2}]$ | $\phantom{-}\frac{49}{31}e^{9} + \frac{382}{31}e^{8} + \frac{282}{31}e^{7} - \frac{3871}{31}e^{6} - \frac{6805}{31}e^{5} + \frac{11185}{31}e^{4} + \frac{23918}{31}e^{3} - \frac{7791}{31}e^{2} - \frac{15478}{31}e + \frac{5521}{31}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $16$ | $[16, 2, -\frac{1}{2}w^{5} + \frac{1}{2}w^{4} + 3w^{3} - \frac{5}{2}w^{2} - 3w + \frac{5}{2}]$ | $-1$ |