Base field 4.4.13725.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 13x^{2} + x + 31\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 78x^{12} + 2141x^{10} - 26070x^{8} + 144894x^{6} - 349228x^{4} + 371864x^{2} - 144500\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -2w^{3} + 6w^{2} + 13w - 26]$ | $\phantom{-}\frac{650275093}{2663701309882}e^{12} - \frac{47949963447}{2663701309882}e^{10} + \frac{34786151284}{78344156173}e^{8} - \frac{5767021738599}{1331850654941}e^{6} + \frac{17813611753886}{1331850654941}e^{4} + \frac{12019469283578}{1331850654941}e^{2} - \frac{2054316073832}{78344156173}$ |
| 11 | $[11, 11, w^{2} - w - 8]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -4w^{3} + 13w^{2} + 23w - 55]$ | $\phantom{-}e$ |
| 16 | $[16, 2, 2]$ | $-1$ |
| 19 | $[19, 19, -w - 1]$ | $...$ |
| 19 | $[19, 19, -w^{3} + 3w^{2} + 7w - 14]$ | $...$ |
| 19 | $[19, 19, w^{3} - 4w^{2} - 5w + 20]$ | $-\frac{970920659}{1331850654941}e^{12} + \frac{74347114626}{1331850654941}e^{10} - \frac{115991788254}{78344156173}e^{8} + \frac{22437855763998}{1331850654941}e^{6} - \frac{107259633607520}{1331850654941}e^{4} + \frac{174812216986407}{1331850654941}e^{2} - \frac{5106860404722}{78344156173}$ |
| 19 | $[19, 19, -3w^{3} + 10w^{2} + 17w - 43]$ | $-\frac{970920659}{1331850654941}e^{12} + \frac{74347114626}{1331850654941}e^{10} - \frac{115991788254}{78344156173}e^{8} + \frac{22437855763998}{1331850654941}e^{6} - \frac{107259633607520}{1331850654941}e^{4} + \frac{174812216986407}{1331850654941}e^{2} - \frac{5106860404722}{78344156173}$ |
| 25 | $[25, 5, -w^{3} + 3w^{2} + 6w - 10]$ | $...$ |
| 29 | $[29, 29, 4w^{3} - 13w^{2} - 23w + 57]$ | $...$ |
| 29 | $[29, 29, w^{2} - w - 6]$ | $...$ |
| 31 | $[31, 31, -2w^{3} + 7w^{2} + 11w - 31]$ | $...$ |
| 31 | $[31, 31, -2w^{3} + 7w^{2} + 11w - 32]$ | $...$ |
| 41 | $[41, 41, 3w^{3} - 10w^{2} - 18w + 43]$ | $...$ |
| 41 | $[41, 41, 3w^{3} - 9w^{2} - 19w + 37]$ | $...$ |
| 41 | $[41, 41, 2w^{3} - 6w^{2} - 11w + 24]$ | $...$ |
| 41 | $[41, 41, -2w^{3} + 7w^{2} + 12w - 33]$ | $...$ |
| 59 | $[59, 59, 3w^{3} - 10w^{2} - 17w + 46]$ | $-\frac{6869743149}{2663701309882}e^{13} + \frac{526738098573}{2663701309882}e^{11} - \frac{7005665945776}{1331850654941}e^{9} + \frac{80305239484483}{1331850654941}e^{7} - \frac{23075277836631}{78344156173}e^{5} + \frac{689739451071805}{1331850654941}e^{3} - \frac{400174729103707}{1331850654941}e$ |
| 59 | $[59, 59, -w^{3} + 4w^{2} + 5w - 17]$ | $-\frac{6869743149}{2663701309882}e^{13} + \frac{526738098573}{2663701309882}e^{11} - \frac{7005665945776}{1331850654941}e^{9} + \frac{80305239484483}{1331850654941}e^{7} - \frac{23075277836631}{78344156173}e^{5} + \frac{689739451071805}{1331850654941}e^{3} - \frac{400174729103707}{1331850654941}e$ |
| 61 | $[61, 61, 4w^{3} - 12w^{2} - 25w + 50]$ | $-\frac{8174717561}{1331850654941}e^{12} + \frac{624952563360}{1331850654941}e^{10} - \frac{972409174109}{78344156173}e^{8} + \frac{187348272264684}{1331850654941}e^{6} - \frac{891338196520282}{1331850654941}e^{4} + \frac{1454214864111316}{1331850654941}e^{2} - \frac{43226027979524}{78344156173}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $16$ | $[16, 2, 2]$ | $1$ |