Base field 5.5.157457.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 5x^{2} + 4x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[27, 27, w^{3} - 2w^{2} - 2w + 3]$ |
| Dimension: | $10$ |
| 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:
| \(x^{10} - 46x^{8} + 786x^{6} - 6301x^{4} + 23875x^{2} - 34347\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w^{2} - w - 2]$ | $\phantom{-}\frac{7}{178}e^{8} - \frac{275}{178}e^{6} + \frac{3681}{178}e^{4} - \frac{10090}{89}e^{2} + \frac{38649}{178}$ |
| 7 | $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}\frac{379}{9523}e^{9} - \frac{15080}{9523}e^{7} + \frac{204055}{9523}e^{5} - \frac{1117561}{9523}e^{3} + \frac{2105930}{9523}e$ |
| 29 | $[29, 29, -w^{4} + 3w^{3} + 2w^{2} - 7w - 1]$ | $\phantom{-}\frac{450}{9523}e^{9} - \frac{17704}{9523}e^{7} + \frac{236000}{9523}e^{5} - \frac{1269505}{9523}e^{3} + \frac{2344785}{9523}e$ |
| 29 | $[29, 29, -w^{2} + 2w + 3]$ | $\phantom{-}\frac{127}{19046}e^{9} - \frac{4023}{19046}e^{7} + \frac{33803}{19046}e^{5} - \frac{15716}{9523}e^{3} - \frac{290867}{19046}e$ |
| 31 | $[31, 31, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $-\frac{154}{9523}e^{9} + \frac{6228}{9523}e^{7} - \frac{86055}{9523}e^{5} + \frac{478047}{9523}e^{3} - \frac{881161}{9523}e$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}\frac{9}{178}e^{8} - \frac{379}{178}e^{6} + \frac{5521}{178}e^{4} - \frac{16393}{89}e^{2} + \frac{66805}{178}$ |
| 32 | $[32, 2, 2]$ | $-\frac{71}{9523}e^{9} + \frac{2624}{9523}e^{7} - \frac{31945}{9523}e^{5} + \frac{151944}{9523}e^{3} - \frac{219809}{9523}e$ |
| 43 | $[43, 43, -w^{2} - w + 4]$ | $-\frac{592}{9523}e^{9} + \frac{22952}{9523}e^{7} - \frac{299890}{9523}e^{5} + \frac{1573393}{9523}e^{3} - \frac{2803449}{9523}e$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 6w^{2} - 2w - 5]$ | $\phantom{-}\frac{7}{89}e^{8} - \frac{275}{89}e^{6} + \frac{3681}{89}e^{4} - \frac{20180}{89}e^{2} + \frac{38649}{89}$ |
| 53 | $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ | $\phantom{-}\frac{7}{89}e^{8} - \frac{275}{89}e^{6} + \frac{3681}{89}e^{4} - \frac{20180}{89}e^{2} + \frac{38649}{89}$ |
| 73 | $[73, 73, w^{4} - w^{3} - 6w^{2} + 2w + 6]$ | $-\frac{142}{9523}e^{9} + \frac{5248}{9523}e^{7} - \frac{63890}{9523}e^{5} + \frac{303888}{9523}e^{3} - \frac{458664}{9523}e$ |
| 73 | $[73, 73, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}\frac{157}{19046}e^{9} - \frac{6473}{19046}e^{7} + \frac{93977}{19046}e^{5} - \frac{288172}{9523}e^{3} + \frac{1246287}{19046}e$ |
| 81 | $[81, 3, 2w^{4} - 5w^{3} - 4w^{2} + 9w + 2]$ | $-\frac{21}{178}e^{8} + \frac{825}{178}e^{6} - \frac{11043}{178}e^{4} + \frac{30181}{89}e^{2} - \frac{113455}{178}$ |
| 83 | $[83, 83, w^{3} - w^{2} - 5w]$ | $-\frac{631}{19046}e^{9} + \frac{26137}{19046}e^{7} - \frac{374307}{19046}e^{5} + \frac{1101845}{9523}e^{3} - \frac{4483681}{19046}e$ |
| 89 | $[89, 89, -w^{4} + 2w^{3} + 4w^{2} - 4w - 2]$ | $-\frac{225}{9523}e^{9} + \frac{8852}{9523}e^{7} - \frac{118000}{9523}e^{5} + \frac{639514}{9523}e^{3} - \frac{1234292}{9523}e$ |
| 97 | $[97, 97, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ | $-\frac{12}{9523}e^{9} + \frac{980}{9523}e^{7} - \frac{22165}{9523}e^{5} + \frac{174159}{9523}e^{3} - \frac{412974}{9523}e$ |
| 101 | $[101, 101, -w^{4} + 3w^{3} + 3w^{2} - 7w - 3]$ | $\phantom{-}\frac{35}{178}e^{8} - \frac{1375}{178}e^{6} + \frac{18227}{178}e^{4} - \frac{48225}{89}e^{2} + \frac{171885}{178}$ |
| 103 | $[103, 103, -w^{4} + w^{3} + 6w^{2} - w - 7]$ | $\phantom{-}e^{2} - 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 1]$ | $-1$ |