Base field 3.3.1229.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 6\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[11, 11, w + 1]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} - 2x^{10} - 14x^{9} + 27x^{8} + 65x^{7} - 122x^{6} - 118x^{5} + 224x^{4} + 59x^{3} - 145x^{2} + 21x + 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2} + 2w - 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w + 3]$ | $\phantom{-}\frac{61}{245}e^{10} - \frac{114}{245}e^{9} - \frac{881}{245}e^{8} + \frac{1419}{245}e^{7} + \frac{4372}{245}e^{6} - \frac{5491}{245}e^{5} - \frac{9111}{245}e^{4} + \frac{7786}{245}e^{3} + \frac{971}{35}e^{2} - \frac{3644}{245}e - \frac{446}{245}$ |
| 4 | $[4, 2, -w^{2} + w + 5]$ | $\phantom{-}\frac{22}{245}e^{10} - \frac{13}{245}e^{9} - \frac{382}{245}e^{8} + \frac{78}{245}e^{7} + \frac{2364}{245}e^{6} + \frac{313}{245}e^{5} - \frac{5997}{245}e^{4} - \frac{1863}{245}e^{3} + \frac{687}{35}e^{2} + \frac{1192}{245}e + \frac{48}{245}$ |
| 9 | $[9, 3, w^{2} + 2w - 1]$ | $\phantom{-}\frac{213}{245}e^{10} - \frac{137}{245}e^{9} - \frac{3253}{245}e^{8} + \frac{1557}{245}e^{7} + \frac{16941}{245}e^{6} - \frac{5578}{245}e^{5} - \frac{35778}{245}e^{4} + \frac{7788}{245}e^{3} + \frac{3573}{35}e^{2} - \frac{4852}{245}e - \frac{248}{245}$ |
| 11 | $[11, 11, w + 1]$ | $\phantom{-}1$ |
| 13 | $[13, 13, -2w^{2} - 3w + 5]$ | $-\frac{141}{245}e^{10} + \frac{139}{245}e^{9} + \frac{2181}{245}e^{8} - \frac{1814}{245}e^{7} - \frac{11632}{245}e^{6} + \frac{7961}{245}e^{5} + \frac{25506}{245}e^{4} - \frac{14286}{245}e^{3} - \frac{2696}{35}e^{2} + \frac{9399}{245}e + \frac{561}{245}$ |
| 17 | $[17, 17, -2w + 5]$ | $\phantom{-}\frac{25}{49}e^{10} - \frac{17}{49}e^{9} - \frac{345}{49}e^{8} + \frac{151}{49}e^{7} + \frac{1546}{49}e^{6} - \frac{239}{49}e^{5} - \frac{2701}{49}e^{4} - \frac{382}{49}e^{3} + \frac{221}{7}e^{2} + \frac{575}{49}e - \frac{39}{49}$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $\phantom{-}\frac{62}{49}e^{10} - \frac{50}{49}e^{9} - \frac{934}{49}e^{8} + \frac{594}{49}e^{7} + \frac{4769}{49}e^{6} - \frac{2245}{49}e^{5} - \frac{9809}{49}e^{4} + \frac{3249}{49}e^{3} + \frac{958}{7}e^{2} - \frac{1808}{49}e - \frac{132}{49}$ |
| 23 | $[23, 23, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{34}{245}e^{10} + \frac{69}{245}e^{9} - \frac{479}{245}e^{8} - \frac{1149}{245}e^{7} + \frac{2228}{245}e^{6} + \frac{6141}{245}e^{5} - \frac{4524}{245}e^{4} - \frac{12256}{245}e^{3} + \frac{559}{35}e^{2} + \frac{7789}{245}e - \frac{594}{245}$ |
| 29 | $[29, 29, 3w^{2} + 6w - 5]$ | $\phantom{-}\frac{424}{245}e^{10} - \frac{451}{245}e^{9} - \frac{5959}{245}e^{8} + \frac{5156}{245}e^{7} + \frac{27698}{245}e^{6} - \frac{17844}{245}e^{5} - \frac{51099}{245}e^{4} + \frac{21514}{245}e^{3} + \frac{4274}{35}e^{2} - \frac{7741}{245}e + \frac{1326}{245}$ |
| 37 | $[37, 37, 4w^{2} - 2w - 25]$ | $\phantom{-}\frac{577}{245}e^{10} - \frac{508}{245}e^{9} - \frac{8727}{245}e^{8} + \frac{5988}{245}e^{7} + \frac{45074}{245}e^{6} - \frac{21937}{245}e^{5} - \frac{94977}{245}e^{4} + \frac{29327}{245}e^{3} + \frac{9712}{35}e^{2} - \frac{14708}{245}e - \frac{2817}{245}$ |
| 67 | $[67, 67, 2w^{2} + 2w - 7]$ | $-\frac{20}{49}e^{10} - \frac{6}{49}e^{9} + \frac{325}{49}e^{8} + \frac{85}{49}e^{7} - \frac{1766}{49}e^{6} - \frac{338}{49}e^{5} + \frac{3670}{49}e^{4} + \frac{482}{49}e^{3} - \frac{307}{7}e^{2} - \frac{166}{49}e - \frac{57}{49}$ |
| 67 | $[67, 67, -2w^{2} - 5w + 1]$ | $\phantom{-}\frac{443}{245}e^{10} - \frac{362}{245}e^{9} - \frac{6868}{245}e^{8} + \frac{4377}{245}e^{7} + \frac{36466}{245}e^{6} - \frac{16538}{245}e^{5} - \frac{78473}{245}e^{4} + \frac{21943}{245}e^{3} + \frac{8108}{35}e^{2} - \frac{9362}{245}e - \frac{3243}{245}$ |
| 67 | $[67, 67, 2w^{2} + 3w - 7]$ | $\phantom{-}\frac{123}{245}e^{10} - \frac{17}{245}e^{9} - \frac{1913}{245}e^{8} - \frac{143}{245}e^{7} + \frac{10366}{245}e^{6} + \frac{2652}{245}e^{5} - \frac{23673}{245}e^{4} - \frac{7977}{245}e^{3} + \frac{2573}{35}e^{2} + \frac{4593}{245}e + \frac{647}{245}$ |
| 71 | $[71, 71, w - 5]$ | $-\frac{29}{245}e^{10} + \frac{6}{245}e^{9} + \frac{214}{245}e^{8} + \frac{209}{245}e^{7} + \frac{492}{245}e^{6} - \frac{2651}{245}e^{5} - \frac{4846}{245}e^{4} + \frac{8191}{245}e^{3} + \frac{916}{35}e^{2} - \frac{6449}{245}e - \frac{531}{245}$ |
| 73 | $[73, 73, w^{2} + 2w - 5]$ | $-\frac{64}{49}e^{10} + \frac{69}{49}e^{9} + \frac{991}{49}e^{8} - \frac{855}{49}e^{7} - \frac{5269}{49}e^{6} + \frac{3299}{49}e^{5} + \frac{11352}{49}e^{4} - \frac{4514}{49}e^{3} - \frac{1170}{7}e^{2} + \frac{2007}{49}e + \frac{533}{49}$ |
| 73 | $[73, 73, 2w^{2} - w - 11]$ | $\phantom{-}\frac{418}{245}e^{10} - \frac{247}{245}e^{9} - \frac{6278}{245}e^{8} + \frac{2707}{245}e^{7} + \frac{31931}{245}e^{6} - \frac{9243}{245}e^{5} - \frac{65678}{245}e^{4} + \frac{12378}{245}e^{3} + \frac{6368}{35}e^{2} - \frac{7977}{245}e + \frac{912}{245}$ |
| 73 | $[73, 73, -2w - 1]$ | $\phantom{-}\frac{57}{245}e^{10} - \frac{223}{245}e^{9} - \frac{767}{245}e^{8} + \frac{3053}{245}e^{7} + \frac{3519}{245}e^{6} - \frac{13477}{245}e^{5} - \frac{6907}{245}e^{4} + \frac{22112}{245}e^{3} + \frac{687}{35}e^{2} - \frac{10988}{245}e + \frac{1728}{245}$ |
| 83 | $[83, 83, 4w^{2} - 31]$ | $-\frac{19}{245}e^{10} + \frac{156}{245}e^{9} - \frac{71}{245}e^{8} - \frac{1916}{245}e^{7} + \frac{2502}{245}e^{6} + \frac{7269}{245}e^{5} - \frac{8886}{245}e^{4} - \frac{9249}{245}e^{3} + \frac{961}{35}e^{2} + \frac{641}{245}e + \frac{894}{245}$ |
| 97 | $[97, 97, 2w^{2} + 2w - 5]$ | $-\frac{36}{35}e^{10} + \frac{69}{35}e^{9} + \frac{501}{35}e^{8} - \frac{834}{35}e^{7} - \frac{2322}{35}e^{6} + \frac{3061}{35}e^{5} + \frac{4226}{35}e^{4} - \frac{3996}{35}e^{3} - \frac{306}{5}e^{2} + \frac{1769}{35}e - \frac{174}{35}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, w + 1]$ | $-1$ |