Base field 3.3.1524.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, 2w^{2} - 6w - 1]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $21$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 5x^{11} - 7x^{10} + 66x^{9} - 23x^{8} - 299x^{7} + 274x^{6} + 557x^{5} - 693x^{4} - 359x^{3} + 594x^{2} + 4x - 106\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + 3w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w^{2} - w + 3]$ | $-\frac{13}{67}e^{11} + \frac{50}{67}e^{10} + \frac{159}{67}e^{9} - \frac{690}{67}e^{8} - \frac{626}{67}e^{7} + \frac{3309}{67}e^{6} + \frac{823}{67}e^{5} - \frac{6647}{67}e^{4} + \frac{154}{67}e^{3} + \frac{5056}{67}e^{2} - \frac{677}{67}e - \frac{828}{67}$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{9}{134}e^{11} - \frac{7}{67}e^{10} - \frac{141}{134}e^{9} + \frac{153}{134}e^{8} + \frac{428}{67}e^{7} - \frac{487}{134}e^{6} - \frac{2487}{134}e^{5} + \frac{211}{67}e^{4} + \frac{3063}{134}e^{3} + \frac{64}{67}e^{2} - \frac{464}{67}e - \frac{69}{67}$ |
| 7 | $[7, 7, 2w^{2} - 6w - 1]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w^{2} + 2w + 4]$ | $-\frac{130}{67}e^{11} + \frac{433}{67}e^{10} + \frac{1657}{67}e^{9} - \frac{5962}{67}e^{8} - \frac{6997}{67}e^{7} + \frac{28735}{67}e^{6} + \frac{10776}{67}e^{5} - \frac{58966}{67}e^{4} - \frac{1676}{67}e^{3} + \frac{47344}{67}e^{2} - \frac{5430}{67}e - \frac{8816}{67}$ |
| 17 | $[17, 17, -w^{2} + 4w - 2]$ | $\phantom{-}\frac{57}{134}e^{11} - \frac{89}{67}e^{10} - \frac{759}{134}e^{9} + \frac{2443}{134}e^{8} + \frac{1728}{67}e^{7} - \frac{11705}{134}e^{6} - \frac{6103}{134}e^{5} + \frac{11900}{67}e^{4} + \frac{2113}{134}e^{3} - \frac{9399}{67}e^{2} + \frac{1260}{67}e + \frac{1707}{67}$ |
| 19 | $[19, 19, w^{2} - 6]$ | $-\frac{329}{134}e^{11} + \frac{576}{67}e^{10} + \frac{3993}{134}e^{9} - \frac{15643}{134}e^{8} - \frac{7710}{67}e^{7} + \frac{74157}{134}e^{6} + \frac{19179}{134}e^{5} - \frac{74944}{67}e^{4} + \frac{5727}{134}e^{3} + \frac{59762}{67}e^{2} - \frac{8193}{67}e - \frac{11637}{67}$ |
| 19 | $[19, 19, -w^{2} - 3w - 1]$ | $-\frac{96}{67}e^{11} + \frac{328}{67}e^{10} + \frac{1169}{67}e^{9} - \frac{4446}{67}e^{8} - \frac{4530}{67}e^{7} + \frac{21029}{67}e^{6} + \frac{5624}{67}e^{5} - \frac{42334}{67}e^{4} + \frac{1900}{67}e^{3} + \frac{33430}{67}e^{2} - \frac{5154}{67}e - \frac{6300}{67}$ |
| 19 | $[19, 19, 3w^{2} - 9w - 1]$ | $\phantom{-}\frac{71}{67}e^{11} - \frac{237}{67}e^{10} - \frac{889}{67}e^{9} + \frac{3217}{67}e^{8} + \frac{3656}{67}e^{7} - \frac{15217}{67}e^{6} - \frac{5438}{67}e^{5} + \frac{30613}{67}e^{4} + \frac{870}{67}e^{3} - \frac{24346}{67}e^{2} + \frac{2208}{67}e + \frac{4852}{67}$ |
| 41 | $[41, 41, w^{2} - 8]$ | $-\frac{56}{67}e^{11} + \frac{169}{67}e^{10} + \frac{788}{67}e^{9} - \frac{2426}{67}e^{8} - \frac{3882}{67}e^{7} + \frac{12306}{67}e^{6} + \frac{7859}{67}e^{5} - \frac{26649}{67}e^{4} - \frac{5078}{67}e^{3} + \frac{22527}{67}e^{2} - \frac{628}{67}e - \frac{4144}{67}$ |
| 43 | $[43, 43, -2w^{2} - 3w + 4]$ | $-\frac{399}{134}e^{11} + \frac{690}{67}e^{10} + \frac{4911}{134}e^{9} - \frac{18709}{134}e^{8} - \frac{9818}{67}e^{7} + \frac{88367}{134}e^{6} + \frac{27579}{134}e^{5} - \frac{88660}{67}e^{4} - \frac{1123}{134}e^{3} + \frac{69746}{67}e^{2} - \frac{7480}{67}e - \frac{13155}{67}$ |
| 47 | $[47, 47, -2w - 3]$ | $-\frac{182}{67}e^{11} + \frac{633}{67}e^{10} + \frac{2226}{67}e^{9} - \frac{8521}{67}e^{8} - \frac{8831}{67}e^{7} + \frac{39827}{67}e^{6} + \frac{12259}{67}e^{5} - \frac{78854}{67}e^{4} + \frac{12}{67}e^{3} + \frac{61203}{67}e^{2} - \frac{7602}{67}e - \frac{11458}{67}$ |
| 49 | $[49, 7, -9w^{2} + 29w - 3]$ | $-\frac{2}{67}e^{11} + \frac{18}{67}e^{10} + \frac{9}{67}e^{9} - \frac{302}{67}e^{8} + \frac{115}{67}e^{7} + \frac{1880}{67}e^{6} - \frac{832}{67}e^{5} - \frac{5223}{67}e^{4} + \frac{1843}{67}e^{3} + \frac{5875}{67}e^{2} - \frac{1573}{67}e - \frac{1488}{67}$ |
| 67 | $[67, 67, 2w - 3]$ | $\phantom{-}\frac{101}{67}e^{11} - \frac{373}{67}e^{10} - \frac{1158}{67}e^{9} + \frac{5000}{67}e^{8} + \frac{3941}{67}e^{7} - \frac{23384}{67}e^{6} - \frac{2874}{67}e^{5} + \frac{46983}{67}e^{4} - \frac{6340}{67}e^{3} - \frac{37900}{67}e^{2} + \frac{7646}{67}e + \frac{7474}{67}$ |
| 71 | $[71, 71, 4w^{2} - 14w + 5]$ | $-\frac{30}{67}e^{11} + \frac{136}{67}e^{10} + \frac{269}{67}e^{9} - \frac{1716}{67}e^{8} - \frac{419}{67}e^{7} + \frac{7363}{67}e^{6} - \frac{1157}{67}e^{5} - \frac{13221}{67}e^{4} + \frac{2922}{67}e^{3} + \frac{8998}{67}e^{2} - \frac{1619}{67}e - \frac{1148}{67}$ |
| 79 | $[79, 79, w^{2} - 3w - 3]$ | $\phantom{-}\frac{261}{134}e^{11} - \frac{471}{67}e^{10} - \frac{3017}{134}e^{9} + \frac{12611}{134}e^{8} + \frac{5243}{67}e^{7} - \frac{58879}{134}e^{6} - \frac{8741}{134}e^{5} + \frac{58982}{67}e^{4} - \frac{13817}{134}e^{3} - \frac{47590}{67}e^{2} + \frac{8654}{67}e + \frac{9791}{67}$ |
| 79 | $[79, 79, -w^{2} + 5w - 5]$ | $\phantom{-}\frac{91}{134}e^{11} - \frac{175}{67}e^{10} - \frac{979}{134}e^{9} + \frac{4361}{134}e^{8} + \frac{1588}{67}e^{7} - \frac{18205}{134}e^{6} - \frac{3483}{134}e^{5} + \frac{15660}{67}e^{4} + \frac{463}{134}e^{3} - \frac{10460}{67}e^{2} + \frac{594}{67}e + \frac{1893}{67}$ |
| 79 | $[79, 79, 6w^{2} - 3w - 38]$ | $-\frac{94}{67}e^{11} + \frac{310}{67}e^{10} + \frac{1227}{67}e^{9} - \frac{4211}{67}e^{8} - \frac{5516}{67}e^{7} + \frac{19819}{67}e^{6} + \frac{10141}{67}e^{5} - \frac{39188}{67}e^{4} - \frac{5638}{67}e^{3} + \frac{29766}{67}e^{2} - \frac{1504}{67}e - \frac{4812}{67}$ |
| 97 | $[97, 97, 3w^{2} - 10w]$ | $-\frac{339}{67}e^{11} + \frac{1175}{67}e^{10} + \frac{4105}{67}e^{9} - \frac{15813}{67}e^{8} - \frac{15917}{67}e^{7} + \frac{74043}{67}e^{6} + \frac{20781}{67}e^{5} - \frac{147394}{67}e^{4} + \frac{2279}{67}e^{3} + \frac{115131}{67}e^{2} - \frac{13665}{67}e - \frac{21066}{67}$ |
| 103 | $[103, 103, 3w^{2} - 4w - 24]$ | $\phantom{-}\frac{197}{134}e^{11} - \frac{317}{67}e^{10} - \frac{2595}{134}e^{9} + \frac{8709}{134}e^{8} + \frac{5877}{67}e^{7} - \frac{41733}{134}e^{6} - \frac{21563}{134}e^{5} + \frac{42280}{67}e^{4} + \frac{11525}{134}e^{3} - \frac{32784}{67}e^{2} + \frac{1509}{67}e + \frac{5279}{67}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, 2w^{2} - 6w - 1]$ | $-1$ |