Base field 5.5.160801.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 4x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[27, 27, w^{4} - w^{3} - 5w^{2} + 4w + 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 48x^{6} + 716x^{4} - 3952x^{2} + 6400\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $\phantom{-}0$ |
| 9 | $[9, 3, -w^{4} + 5w^{2} - 3]$ | $-\frac{5}{272}e^{6} + \frac{12}{17}e^{4} - \frac{441}{68}e^{2} + \frac{231}{17}$ |
| 9 | $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $-\frac{49}{5440}e^{7} + \frac{259}{680}e^{5} - \frac{5811}{1360}e^{3} + \frac{4093}{340}e$ |
| 17 | $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $-\frac{1}{272}e^{6} + \frac{13}{68}e^{4} - \frac{197}{68}e^{2} + \frac{206}{17}$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w - 2]$ | $\phantom{-}\frac{21}{5440}e^{7} - \frac{111}{680}e^{5} + \frac{2539}{1360}e^{3} - \frac{1827}{340}e$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $-\frac{43}{5440}e^{7} + \frac{203}{680}e^{5} - \frac{3337}{1360}e^{3} + \frac{511}{340}e$ |
| 31 | $[31, 31, w^{3} - 4w + 2]$ | $\phantom{-}\frac{3}{136}e^{6} - \frac{61}{68}e^{4} + \frac{319}{34}e^{2} - \frac{335}{17}$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}\frac{19}{5440}e^{7} - \frac{8}{85}e^{5} - \frac{99}{1360}e^{3} + \frac{2257}{340}e$ |
| 37 | $[37, 37, w^{3} - 3w - 1]$ | $\phantom{-}\frac{1}{136}e^{6} - \frac{13}{34}e^{4} + \frac{197}{34}e^{2} - \frac{344}{17}$ |
| 53 | $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ | $\phantom{-}\frac{5}{1088}e^{7} - \frac{3}{17}e^{5} + \frac{475}{272}e^{3} - \frac{333}{68}e$ |
| 59 | $[59, 59, -w^{4} + 5w^{2} + w - 4]$ | $-\frac{43}{2720}e^{7} + \frac{203}{340}e^{5} - \frac{3677}{680}e^{3} + \frac{1871}{170}e$ |
| 61 | $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ | $-\frac{11}{2720}e^{7} + \frac{23}{170}e^{5} - \frac{569}{680}e^{3} - \frac{63}{170}e$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ | $\phantom{-}\frac{21}{1360}e^{7} - \frac{111}{170}e^{5} + \frac{2539}{340}e^{3} - \frac{1827}{85}e$ |
| 71 | $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ | $\phantom{-}\frac{3}{136}e^{6} - \frac{61}{68}e^{4} + \frac{151}{17}e^{2} - \frac{216}{17}$ |
| 79 | $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ | $\phantom{-}\frac{11}{5440}e^{7} - \frac{23}{340}e^{5} + \frac{229}{1360}e^{3} + \frac{913}{340}e$ |
| 83 | $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ | $\phantom{-}\frac{1}{16}e^{6} - \frac{5}{2}e^{4} + \frac{103}{4}e^{2} - 64$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ | $-\frac{1}{272}e^{7} + \frac{13}{68}e^{5} - \frac{107}{34}e^{3} + \frac{497}{34}e$ |
| 83 | $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ | $\phantom{-}\frac{1}{5440}e^{7} + \frac{19}{680}e^{5} - \frac{1401}{1360}e^{3} + \frac{1953}{340}e$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ | $-\frac{1}{68}e^{6} + \frac{13}{17}e^{4} - \frac{197}{17}e^{2} + \frac{722}{17}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $-1$ |