Base field \(\Q(\sqrt{321}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 80\); narrow class number \(6\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[2, 2, w]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 3x^{7} + 10x^{6} - 11x^{5} + 25x^{4} - 25x^{3} + 46x^{2} - 21x + 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{1042}{19011}e^{7} - \frac{1050}{6337}e^{6} + \frac{10675}{19011}e^{5} - \frac{11270}{19011}e^{4} + \frac{24850}{19011}e^{3} - \frac{17500}{19011}e^{2} + \frac{45124}{19011}e - \frac{6862}{6337}$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -2w + 19]$ | $\phantom{-}\frac{98}{6337}e^{7} + \frac{543}{6337}e^{6} - \frac{784}{6337}e^{5} + \frac{4900}{6337}e^{4} - \frac{59}{6337}e^{3} + \frac{11466}{6337}e^{2} - \frac{5292}{6337}e + \frac{16114}{6337}$ |
| 5 | $[5, 5, w]$ | $-\frac{266}{6337}e^{7} + \frac{1242}{6337}e^{6} - \frac{4209}{6337}e^{5} + \frac{5711}{6337}e^{4} - \frac{9798}{6337}e^{3} + \frac{6900}{6337}e^{2} - \frac{17321}{6337}e + \frac{621}{6337}$ |
| 5 | $[5, 5, w + 4]$ | $-\frac{1781}{6337}e^{7} + \frac{5457}{6337}e^{6} - \frac{17437}{6337}e^{5} + \frac{18679}{6337}e^{4} - \frac{38825}{6337}e^{3} + \frac{38766}{6337}e^{2} - \frac{68588}{6337}e + \frac{31245}{6337}$ |
| 13 | $[13, 13, w + 1]$ | $\phantom{-}\frac{7802}{19011}e^{7} - \frac{8093}{6337}e^{6} + \frac{70661}{19011}e^{5} - \frac{78838}{19011}e^{4} + \frac{151400}{19011}e^{3} - \frac{202478}{19011}e^{2} + \frac{256751}{19011}e - \frac{38900}{6337}$ |
| 13 | $[13, 13, w + 11]$ | $\phantom{-}\frac{61}{19011}e^{7} + \frac{48}{6337}e^{6} - \frac{488}{19011}e^{5} - \frac{3287}{19011}e^{4} - \frac{1136}{19011}e^{3} + \frac{800}{19011}e^{2} - \frac{53990}{19011}e + \frac{24}{6337}$ |
| 17 | $[17, 17, w + 3]$ | $\phantom{-}\frac{3819}{6337}e^{7} - \frac{9684}{6337}e^{6} + \frac{32818}{6337}e^{5} - \frac{24508}{6337}e^{4} + \frac{76396}{6337}e^{3} - \frac{53800}{6337}e^{2} + \frac{123298}{6337}e - \frac{4842}{6337}$ |
| 17 | $[17, 17, w + 13]$ | $-\frac{2504}{6337}e^{7} + \frac{7594}{6337}e^{6} - \frac{24327}{6337}e^{5} + \frac{26888}{6337}e^{4} - \frac{58500}{6337}e^{3} + \frac{61904}{6337}e^{2} - \frac{105590}{6337}e + \frac{48156}{6337}$ |
| 19 | $[19, 19, w + 6]$ | $\phantom{-}\frac{61}{19011}e^{7} + \frac{48}{6337}e^{6} - \frac{488}{19011}e^{5} - \frac{3287}{19011}e^{4} - \frac{1136}{19011}e^{3} + \frac{800}{19011}e^{2} - \frac{92012}{19011}e + \frac{24}{6337}$ |
| 19 | $[19, 19, w + 12]$ | $-\frac{994}{19011}e^{7} + \frac{880}{6337}e^{6} - \frac{11059}{19011}e^{5} + \frac{13670}{19011}e^{4} - \frac{41950}{19011}e^{3} + \frac{23116}{19011}e^{2} - \frac{85738}{19011}e + \frac{13114}{6337}$ |
| 37 | $[37, 37, w + 2]$ | $\phantom{-}\frac{9556}{19011}e^{7} - \frac{7440}{6337}e^{6} + \frac{75640}{19011}e^{5} - \frac{41834}{19011}e^{4} + \frac{176080}{19011}e^{3} - \frac{124000}{19011}e^{2} + \frac{307786}{19011}e - \frac{3720}{6337}$ |
| 37 | $[37, 37, w + 34]$ | $\phantom{-}\frac{9923}{19011}e^{7} - \frac{10060}{6337}e^{6} + \frac{91715}{19011}e^{5} - \frac{105865}{19011}e^{4} + \frac{227525}{19011}e^{3} - \frac{296519}{19011}e^{2} + \frac{408371}{19011}e - \frac{62063}{6337}$ |
| 49 | $[49, 7, -7]$ | $-\frac{98}{6337}e^{7} - \frac{543}{6337}e^{6} + \frac{784}{6337}e^{5} - \frac{4900}{6337}e^{4} + \frac{59}{6337}e^{3} - \frac{11466}{6337}e^{2} + \frac{5292}{6337}e - \frac{73147}{6337}$ |
| 59 | $[59, 59, -4w - 33]$ | $\phantom{-}\frac{495}{6337}e^{7} + \frac{3454}{6337}e^{6} - \frac{3960}{6337}e^{5} + \frac{24750}{6337}e^{4} + \frac{5845}{6337}e^{3} + \frac{57915}{6337}e^{2} - \frac{26730}{6337}e + \frac{65097}{6337}$ |
| 59 | $[59, 59, 4w - 37]$ | $-\frac{90}{6337}e^{7} - \frac{628}{6337}e^{6} + \frac{720}{6337}e^{5} - \frac{4500}{6337}e^{4} + \frac{3546}{6337}e^{3} - \frac{10530}{6337}e^{2} + \frac{4860}{6337}e - \frac{6651}{6337}$ |
| 61 | $[61, 61, w + 28]$ | $-\frac{4120}{19011}e^{7} + \frac{4030}{6337}e^{6} - \frac{43084}{19011}e^{5} + \frac{47480}{19011}e^{4} - \frac{116500}{19011}e^{3} + \frac{132649}{19011}e^{2} - \frac{221110}{19011}e + \frac{33700}{6337}$ |
| 61 | $[61, 61, w + 32]$ | $\phantom{-}\frac{14278}{19011}e^{7} - \frac{13074}{6337}e^{6} + \frac{132919}{19011}e^{5} - \frac{109910}{19011}e^{4} + \frac{309418}{19011}e^{3} - \frac{217900}{19011}e^{2} + \frac{585106}{19011}e - \frac{6537}{6337}$ |
| 71 | $[71, 71, w + 22]$ | $-\frac{388}{6337}e^{7} + \frac{954}{6337}e^{6} - \frac{3233}{6337}e^{5} - \frac{389}{6337}e^{4} - \frac{7526}{6337}e^{3} + \frac{5300}{6337}e^{2} - \frac{48755}{6337}e + \frac{477}{6337}$ |
| 71 | $[71, 71, w + 48]$ | $\phantom{-}\frac{739}{6337}e^{7} - \frac{2307}{6337}e^{6} + \frac{6762}{6337}e^{5} - \frac{7409}{6337}e^{4} + \frac{13975}{6337}e^{3} - \frac{2255}{6337}e^{2} + \frac{23464}{6337}e - \frac{10659}{6337}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-\frac{1042}{19011}e^{7} + \frac{1050}{6337}e^{6} - \frac{10675}{19011}e^{5} + \frac{11270}{19011}e^{4} - \frac{24850}{19011}e^{3} + \frac{17500}{19011}e^{2} - \frac{45124}{19011}e + \frac{6862}{6337}$ |