Base field 3.3.1901.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 4\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[9, 3, -w^{2} + 2w + 7]$ |
Dimension: | $12$ |
CM: | no |
Base change: | no |
Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{12} + 3x^{11} - 13x^{10} - 44x^{9} + 52x^{8} + 229x^{7} - 44x^{6} - 505x^{5} - 110x^{4} + 453x^{3} + 161x^{2} - 139x - 51\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w + 2]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 1]$ | $-\frac{5}{23}e^{11} - \frac{6}{23}e^{10} + \frac{85}{23}e^{9} + \frac{90}{23}e^{8} - \frac{537}{23}e^{7} - \frac{482}{23}e^{6} + \frac{1543}{23}e^{5} + \frac{1123}{23}e^{4} - \frac{1959}{23}e^{3} - \frac{1140}{23}e^{2} + \frac{833}{23}e + \frac{364}{23}$ |
4 | $[4, 2, -w^{2} + 3w + 3]$ | $\phantom{-}\frac{5}{23}e^{11} + \frac{6}{23}e^{10} - \frac{85}{23}e^{9} - \frac{90}{23}e^{8} + \frac{537}{23}e^{7} + \frac{482}{23}e^{6} - \frac{1543}{23}e^{5} - \frac{1100}{23}e^{4} + \frac{1959}{23}e^{3} + \frac{1002}{23}e^{2} - \frac{833}{23}e - \frac{272}{23}$ |
9 | $[9, 3, -w^{2} + 2w + 7]$ | $-1$ |
13 | $[13, 13, w + 3]$ | $-\frac{58}{23}e^{11} - \frac{88}{23}e^{10} + \frac{894}{23}e^{9} + \frac{1251}{23}e^{8} - \frac{5001}{23}e^{7} - \frac{6226}{23}e^{6} + \frac{12319}{23}e^{5} + \frac{12760}{23}e^{4} - \frac{13046}{23}e^{3} - \frac{9981}{23}e^{2} + \frac{4842}{23}e + \frac{2318}{23}$ |
13 | $[13, 13, -w + 3]$ | $\phantom{-}\frac{56}{23}e^{11} + \frac{81}{23}e^{10} - \frac{860}{23}e^{9} - \frac{1146}{23}e^{8} + \frac{4777}{23}e^{7} + \frac{5656}{23}e^{6} - \frac{11619}{23}e^{5} - \frac{11423}{23}e^{4} + \frac{12037}{23}e^{3} + \frac{8766}{23}e^{2} - \frac{4311}{23}e - \frac{2108}{23}$ |
13 | $[13, 13, -w + 1]$ | $-\frac{2}{23}e^{11} - \frac{7}{23}e^{10} + \frac{34}{23}e^{9} + \frac{105}{23}e^{8} - \frac{224}{23}e^{7} - \frac{570}{23}e^{6} + \frac{700}{23}e^{5} + \frac{1337}{23}e^{4} - \frac{1009}{23}e^{3} - \frac{1238}{23}e^{2} + \frac{554}{23}e + \frac{302}{23}$ |
17 | $[17, 17, -w^{2} - 2w + 1]$ | $-\frac{79}{23}e^{11} - \frac{127}{23}e^{10} + \frac{1205}{23}e^{9} + \frac{1790}{23}e^{8} - \frac{6617}{23}e^{7} - \frac{8761}{23}e^{6} + \frac{15759}{23}e^{5} + \frac{17357}{23}e^{4} - \frac{15717}{23}e^{3} - \frac{12653}{23}e^{2} + \frac{5392}{23}e + \frac{2637}{23}$ |
23 | $[23, 23, w^{2} - 2w - 5]$ | $-\frac{9}{23}e^{11} - \frac{20}{23}e^{10} + \frac{130}{23}e^{9} + \frac{277}{23}e^{8} - \frac{663}{23}e^{7} - \frac{1323}{23}e^{6} + \frac{1425}{23}e^{5} + \frac{2532}{23}e^{4} - \frac{1263}{23}e^{3} - \frac{1799}{23}e^{2} + \frac{446}{23}e + \frac{393}{23}$ |
31 | $[31, 31, 2w + 3]$ | $-\frac{47}{23}e^{11} - \frac{61}{23}e^{10} + \frac{730}{23}e^{9} + \frac{869}{23}e^{8} - \frac{4091}{23}e^{7} - \frac{4310}{23}e^{6} + \frac{9987}{23}e^{5} + \frac{8730}{23}e^{4} - \frac{10291}{23}e^{3} - \frac{6737}{23}e^{2} + \frac{3658}{23}e + \frac{1646}{23}$ |
31 | $[31, 31, -2w^{2} + 3w + 15]$ | $\phantom{-}\frac{5}{23}e^{11} + \frac{6}{23}e^{10} - \frac{85}{23}e^{9} - \frac{90}{23}e^{8} + \frac{537}{23}e^{7} + \frac{505}{23}e^{6} - \frac{1543}{23}e^{5} - \frac{1307}{23}e^{4} + \frac{1959}{23}e^{3} + \frac{1462}{23}e^{2} - \frac{833}{23}e - \frac{433}{23}$ |
31 | $[31, 31, 3w + 7]$ | $\phantom{-}\frac{19}{23}e^{11} + \frac{32}{23}e^{10} - \frac{277}{23}e^{9} - \frac{457}{23}e^{8} + \frac{1392}{23}e^{7} + \frac{2241}{23}e^{6} - \frac{2763}{23}e^{5} - \frac{4318}{23}e^{4} + \frac{1846}{23}e^{3} + \frac{2791}{23}e^{2} - \frac{341}{23}e - \frac{431}{23}$ |
37 | $[37, 37, 3w^{2} - 4w - 27]$ | $-\frac{108}{23}e^{11} - \frac{171}{23}e^{10} + \frac{1629}{23}e^{9} + \frac{2404}{23}e^{8} - \frac{8807}{23}e^{7} - \frac{11713}{23}e^{6} + \frac{20550}{23}e^{5} + \frac{22978}{23}e^{4} - \frac{20124}{23}e^{3} - \frac{16344}{23}e^{2} + \frac{7054}{23}e + \frac{3290}{23}$ |
41 | $[41, 41, -2w^{2} + 7w + 1]$ | $-\frac{96}{23}e^{11} - \frac{152}{23}e^{10} + \frac{1471}{23}e^{9} + \frac{2165}{23}e^{8} - \frac{8130}{23}e^{7} - \frac{10754}{23}e^{6} + \frac{19593}{23}e^{5} + \frac{21833}{23}e^{4} - \frac{20050}{23}e^{3} - \frac{16713}{23}e^{2} + \frac{7180}{23}e + \frac{3801}{23}$ |
59 | $[59, 59, w^{2} - 3]$ | $-\frac{88}{23}e^{11} - \frac{124}{23}e^{10} + \frac{1358}{23}e^{9} + \frac{1745}{23}e^{8} - \frac{7602}{23}e^{7} - \frac{8589}{23}e^{6} + \frac{18725}{23}e^{5} + \frac{17428}{23}e^{4} - \frac{19786}{23}e^{3} - \frac{13693}{23}e^{2} + \frac{7218}{23}e + \frac{3375}{23}$ |
61 | $[61, 61, 4w^{2} - 12w - 11]$ | $-\frac{84}{23}e^{11} - \frac{156}{23}e^{10} + \frac{1244}{23}e^{9} + \frac{2202}{23}e^{8} - \frac{6533}{23}e^{7} - \frac{10784}{23}e^{6} + \frac{14519}{23}e^{5} + \frac{21309}{23}e^{4} - \frac{13191}{23}e^{3} - \frac{15288}{23}e^{2} + \frac{4477}{23}e + \frac{3047}{23}$ |
71 | $[71, 71, w^{2} - 2w - 11]$ | $\phantom{-}\frac{118}{23}e^{11} + \frac{206}{23}e^{10} - \frac{1776}{23}e^{9} - \frac{2906}{23}e^{8} + \frac{9582}{23}e^{7} + \frac{14241}{23}e^{6} - \frac{22325}{23}e^{5} - \frac{28260}{23}e^{4} + \frac{21926}{23}e^{3} + \frac{20602}{23}e^{2} - \frac{7846}{23}e - \frac{4248}{23}$ |
97 | $[97, 97, 3w + 5]$ | $\phantom{-}\frac{154}{23}e^{11} + \frac{240}{23}e^{10} - \frac{2342}{23}e^{9} - \frac{3370}{23}e^{8} + \frac{12832}{23}e^{7} + \frac{16451}{23}e^{6} - \frac{30601}{23}e^{5} - \frac{32615}{23}e^{4} + \frac{30934}{23}e^{3} + \frac{24049}{23}e^{2} - \frac{11033}{23}e - \frac{5360}{23}$ |
101 | $[101, 101, 2w^{2} - 6w - 7]$ | $\phantom{-}\frac{37}{23}e^{11} + \frac{72}{23}e^{10} - \frac{537}{23}e^{9} - \frac{988}{23}e^{8} + \frac{2764}{23}e^{7} + \frac{4680}{23}e^{6} - \frac{5981}{23}e^{5} - \frac{8899}{23}e^{4} + \frac{5039}{23}e^{3} + \frac{6205}{23}e^{2} - \frac{1233}{23}e - \frac{1263}{23}$ |
103 | $[103, 103, 2w^{2} - 3w - 19]$ | $\phantom{-}\frac{198}{23}e^{11} + \frac{302}{23}e^{10} - \frac{3044}{23}e^{9} - \frac{4300}{23}e^{8} + \frac{16932}{23}e^{7} + \frac{21401}{23}e^{6} - \frac{41286}{23}e^{5} - \frac{43721}{23}e^{4} + \frac{43127}{23}e^{3} + \frac{33897}{23}e^{2} - \frac{16022}{23}e - \frac{7726}{23}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$9$ | $[9, 3, -w^{2} + 2w + 7]$ | $1$ |