Base field 3.3.985.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[23, 23, -w^{2} + 3]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} + x^{8} - 30x^{7} - 20x^{6} + 307x^{5} + 89x^{4} - 1188x^{3} + 122x^{2} + 1118x - 304\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}\frac{523}{9104}e^{8} - \frac{357}{4552}e^{7} - \frac{3113}{2276}e^{6} + \frac{1175}{569}e^{5} + \frac{80097}{9104}e^{4} - \frac{32439}{2276}e^{3} - \frac{10431}{1138}e^{2} + \frac{67731}{4552}e - \frac{1205}{569}$ |
| 7 | $[7, 7, -w + 2]$ | $\phantom{-}\frac{359}{9104}e^{8} - \frac{283}{2276}e^{7} - \frac{4055}{4552}e^{6} + \frac{13993}{4552}e^{5} + \frac{42963}{9104}e^{4} - \frac{23219}{1138}e^{3} + \frac{6463}{2276}e^{2} + \frac{103773}{4552}e - \frac{5130}{569}$ |
| 8 | $[8, 2, 2]$ | $-\frac{179}{9104}e^{8} + \frac{157}{4552}e^{7} + \frac{961}{2276}e^{6} - \frac{949}{1138}e^{5} - \frac{17361}{9104}e^{4} + \frac{11703}{2276}e^{3} - \frac{4335}{1138}e^{2} - \frac{12267}{4552}e + \frac{3512}{569}$ |
| 11 | $[11, 11, -w^{2} + 2w + 2]$ | $-\frac{17}{2276}e^{8} + \frac{33}{2276}e^{7} + \frac{173}{1138}e^{6} - \frac{845}{2276}e^{5} - \frac{1261}{2276}e^{4} + \frac{1210}{569}e^{3} - \frac{2877}{1138}e^{2} + \frac{1467}{1138}e + \frac{2078}{569}$ |
| 17 | $[17, 17, -w - 3]$ | $-\frac{693}{9104}e^{8} + \frac{1091}{4552}e^{7} + \frac{1989}{1138}e^{6} - \frac{3339}{569}e^{5} - \frac{88155}{9104}e^{4} + \frac{87783}{2276}e^{3} - \frac{2167}{1138}e^{2} - \frac{191897}{4552}e + \frac{5831}{569}$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{249}{4552}e^{8} - \frac{79}{1138}e^{7} - \frac{759}{569}e^{6} + \frac{4063}{2276}e^{5} + \frac{41163}{4552}e^{4} - \frac{13673}{1138}e^{3} - \frac{13589}{1138}e^{2} + \frac{28317}{2276}e - \frac{759}{569}$ |
| 17 | $[17, 17, -w^{2} + w + 4]$ | $-\frac{43}{9104}e^{8} + \frac{25}{4552}e^{7} + \frac{269}{2276}e^{6} - \frac{52}{569}e^{5} - \frac{7273}{9104}e^{4} - \frac{253}{2276}e^{3} + \frac{1419}{1138}e^{2} + \frac{21517}{4552}e + \frac{494}{569}$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}1$ |
| 27 | $[27, 3, -3]$ | $\phantom{-}\frac{93}{9104}e^{8} - \frac{107}{4552}e^{7} - \frac{423}{2276}e^{6} + \frac{741}{1138}e^{5} + \frac{2815}{9104}e^{4} - \frac{12209}{2276}e^{3} + \frac{6035}{1138}e^{2} + \frac{50749}{4552}e - \frac{3093}{569}$ |
| 29 | $[29, 29, w^{2} - w - 8]$ | $\phantom{-}\frac{767}{4552}e^{8} - \frac{1355}{4552}e^{7} - \frac{18121}{4552}e^{6} + \frac{34041}{4552}e^{5} + \frac{14061}{569}e^{4} - \frac{112833}{2276}e^{3} - \frac{41499}{2276}e^{2} + \frac{56189}{1138}e - \frac{7884}{569}$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $-\frac{677}{9104}e^{8} + \frac{473}{4552}e^{7} + \frac{3997}{2276}e^{6} - \frac{5961}{2276}e^{5} - \frac{99687}{9104}e^{4} + \frac{39049}{2276}e^{3} + \frac{5196}{569}e^{2} - \frac{64349}{4552}e + \frac{2564}{569}$ |
| 29 | $[29, 29, w^{2} - w - 1]$ | $-\frac{679}{9104}e^{8} + \frac{977}{4552}e^{7} + \frac{3639}{2276}e^{6} - \frac{6181}{1138}e^{5} - \frac{68373}{9104}e^{4} + \frac{83975}{2276}e^{3} - \frac{11733}{1138}e^{2} - \frac{193239}{4552}e + \frac{9587}{569}$ |
| 31 | $[31, 31, w^{2} - 2]$ | $-\frac{309}{9104}e^{8} + \frac{121}{1138}e^{7} + \frac{3747}{4552}e^{6} - \frac{11445}{4552}e^{5} - \frac{47421}{9104}e^{4} + \frac{9063}{569}e^{3} + \frac{6169}{2276}e^{2} - \frac{77027}{4552}e + \frac{5945}{569}$ |
| 37 | $[37, 37, 2w - 5]$ | $-\frac{839}{9104}e^{8} + \frac{449}{2276}e^{7} + \frac{9743}{4552}e^{6} - \frac{22977}{4552}e^{5} - \frac{115787}{9104}e^{4} + \frac{39565}{1138}e^{3} + \frac{11561}{2276}e^{2} - \frac{188469}{4552}e + \frac{10962}{569}$ |
| 43 | $[43, 43, w^{2} - 2w - 5]$ | $\phantom{-}\frac{627}{9104}e^{8} - \frac{120}{569}e^{7} - \frac{7117}{4552}e^{6} + \frac{23599}{4552}e^{5} + \frac{73419}{9104}e^{4} - \frac{19307}{569}e^{3} + \frac{17225}{2276}e^{2} + \frac{152541}{4552}e - \frac{9638}{569}$ |
| 47 | $[47, 47, w^{2} - 3w - 2]$ | $-\frac{1053}{9104}e^{8} + \frac{771}{4552}e^{7} + \frac{6111}{2276}e^{6} - \frac{5233}{1138}e^{5} - \frac{148463}{9104}e^{4} + \frac{75317}{2276}e^{3} + \frac{11989}{1138}e^{2} - \frac{183725}{4552}e + \frac{7360}{569}$ |
| 49 | $[49, 7, w^{2} + w - 4]$ | $\phantom{-}\frac{497}{4552}e^{8} - \frac{633}{2276}e^{7} - \frac{5861}{2276}e^{6} + \frac{7975}{1138}e^{5} + \frac{71809}{4552}e^{4} - \frac{27193}{569}e^{3} - \frac{5590}{569}e^{2} + \frac{132163}{2276}e - \frac{4737}{569}$ |
| 53 | $[53, 53, w^{2} - 2w - 6]$ | $\phantom{-}\frac{427}{4552}e^{8} - \frac{158}{569}e^{7} - \frac{4747}{2276}e^{6} + \frac{15683}{2276}e^{5} + \frac{48007}{4552}e^{4} - \frac{26208}{569}e^{3} + \frac{11079}{1138}e^{2} + \frac{118389}{2276}e - \frac{10433}{569}$ |
| 71 | $[71, 71, w - 5]$ | $\phantom{-}\frac{1665}{9104}e^{8} - \frac{967}{2276}e^{7} - \frac{20157}{4552}e^{6} + \frac{48091}{4552}e^{5} + \frac{263277}{9104}e^{4} - \frac{81345}{1138}e^{3} - \frac{69491}{2276}e^{2} + \frac{400619}{4552}e - \frac{4440}{569}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, -w^{2} + 3]$ | $-1$ |