Base field 4.4.17417.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 3x + 4\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[17, 17, -w^{2} + 3w + 1]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $42$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 22x^{10} + 182x^{8} - 709x^{6} + 1320x^{4} - 1036x^{2} + 196\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{3} - 3w^{2} - w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - 2w - 3]$ | $-\frac{23}{490}e^{11} + \frac{246}{245}e^{9} - \frac{54}{7}e^{7} + \frac{12387}{490}e^{5} - \frac{7767}{245}e^{3} + \frac{319}{35}e$ |
| 5 | $[5, 5, w^{3} - 3w^{2} - 3w + 5]$ | $\phantom{-}\frac{11}{70}e^{10} - \frac{107}{35}e^{8} + 21e^{6} - \frac{4229}{70}e^{4} + \frac{2199}{35}e^{2} - \frac{43}{5}$ |
| 8 | $[8, 2, w^{3} - 2w^{2} - 3w + 3]$ | $-\frac{8}{245}e^{11} + \frac{289}{490}e^{9} - \frac{26}{7}e^{7} + \frac{2487}{245}e^{5} - \frac{6343}{490}e^{3} + \frac{263}{35}e$ |
| 13 | $[13, 13, -w^{2} + w + 3]$ | $-\frac{31}{245}e^{11} + \frac{1273}{490}e^{9} - \frac{134}{7}e^{7} + \frac{14874}{245}e^{5} - \frac{36921}{490}e^{3} + \frac{761}{35}e$ |
| 17 | $[17, 17, -w^{2} + 3w + 1]$ | $-1$ |
| 23 | $[23, 23, w^{2} - 3]$ | $-\frac{67}{490}e^{11} + \frac{674}{245}e^{9} - \frac{136}{7}e^{7} + \frac{27413}{490}e^{5} - \frac{12783}{245}e^{3} - \frac{104}{35}e$ |
| 25 | $[25, 5, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{25}{98}e^{11} - \frac{473}{98}e^{9} + \frac{225}{7}e^{7} - \frac{8905}{98}e^{5} + \frac{9865}{98}e^{3} - \frac{204}{7}e$ |
| 37 | $[37, 37, w^{3} - 4w^{2} - 2w + 9]$ | $\phantom{-}\frac{11}{245}e^{11} - \frac{214}{245}e^{9} + \frac{41}{7}e^{7} - \frac{3634}{245}e^{5} + \frac{1283}{245}e^{3} + \frac{614}{35}e$ |
| 41 | $[41, 41, w^{2} - w - 5]$ | $-\frac{19}{98}e^{11} + \frac{383}{98}e^{9} - \frac{199}{7}e^{7} + \frac{8865}{98}e^{5} - \frac{11437}{98}e^{3} + \frac{283}{7}e$ |
| 49 | $[49, 7, -w^{3} + 2w^{2} + 2w - 1]$ | $-\frac{32}{245}e^{11} + \frac{1401}{490}e^{9} - \frac{160}{7}e^{7} + \frac{19748}{245}e^{5} - \frac{57467}{490}e^{3} + \frac{1752}{35}e$ |
| 49 | $[49, 7, w^{2} + w - 3]$ | $\phantom{-}\frac{53}{245}e^{11} - \frac{2129}{490}e^{9} + \frac{216}{7}e^{7} - \frac{22387}{245}e^{5} + \frac{46953}{490}e^{3} - \frac{338}{35}e$ |
| 59 | $[59, 59, w^{3} - 3w^{2} - 4w + 5]$ | $\phantom{-}\frac{3}{35}e^{10} - \frac{52}{35}e^{8} + 8e^{6} - \frac{412}{35}e^{4} - \frac{401}{35}e^{2} + \frac{87}{5}$ |
| 67 | $[67, 67, -w^{3} + 3w^{2} + w - 5]$ | $\phantom{-}\frac{4}{35}e^{10} - \frac{81}{35}e^{8} + 17e^{6} - \frac{1926}{35}e^{4} + \frac{2627}{35}e^{2} - \frac{149}{5}$ |
| 71 | $[71, 71, 2w - 3]$ | $-\frac{37}{245}e^{11} + \frac{1551}{490}e^{9} - \frac{164}{7}e^{7} + \frac{17413}{245}e^{5} - \frac{35737}{490}e^{3} + \frac{232}{35}e$ |
| 71 | $[71, 71, w^{3} - 4w^{2} + 2w + 5]$ | $\phantom{-}\frac{19}{70}e^{10} - \frac{188}{35}e^{8} + 38e^{6} - \frac{8081}{70}e^{4} + \frac{4756}{35}e^{2} - \frac{162}{5}$ |
| 79 | $[79, 79, -w^{3} + 5w^{2} - 4w - 5]$ | $-\frac{1}{70}e^{11} - \frac{3}{35}e^{9} + 4e^{7} - \frac{1741}{70}e^{5} + \frac{1671}{35}e^{3} - \frac{112}{5}e$ |
| 79 | $[79, 79, -2w^{3} + 7w^{2} + 5w - 15]$ | $-\frac{17}{98}e^{11} + \frac{353}{98}e^{9} - \frac{188}{7}e^{7} + \frac{8427}{98}e^{5} - \frac{10491}{98}e^{3} + \frac{244}{7}e$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{18}{35}e^{10} - \frac{347}{35}e^{8} + 67e^{6} - \frac{6602}{35}e^{4} + \frac{6869}{35}e^{2} - \frac{213}{5}$ |
| 83 | $[83, 83, -2w^{3} + 6w^{2} + 2w - 5]$ | $\phantom{-}\frac{169}{490}e^{11} - \frac{1733}{245}e^{9} + \frac{363}{7}e^{7} - \frac{79641}{490}e^{5} + \frac{48666}{245}e^{3} - \frac{2172}{35}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $17$ | $[17, 17, -w^{2} + 3w + 1]$ | $1$ |