Base field 3.3.697.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[27, 3, -3]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 42x^{8} + 688x^{6} - 5482x^{4} + 21191x^{2} - 31684\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $-\frac{1}{8}e^{8} + \frac{35}{8}e^{6} - \frac{443}{8}e^{4} + \frac{2389}{8}e^{2} - \frac{1149}{2}$ |
| 11 | $[11, 11, -w^{2} + 2w + 4]$ | $-\frac{1}{4}e^{6} + 6e^{4} - \frac{175}{4}e^{2} + 93$ |
| 11 | $[11, 11, -w + 2]$ | $\phantom{-}\frac{35}{712}e^{9} - \frac{1203}{712}e^{7} + \frac{14913}{712}e^{5} - \frac{78573}{712}e^{3} + \frac{36947}{178}e$ |
| 11 | $[11, 11, w - 1]$ | $\phantom{-}\frac{35}{712}e^{9} - \frac{1203}{712}e^{7} + \frac{14913}{712}e^{5} - \frac{78573}{712}e^{3} + \frac{36947}{178}e$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $-\frac{31}{712}e^{9} + \frac{1035}{712}e^{7} - \frac{12517}{712}e^{5} + \frac{64477}{712}e^{3} - \frac{29373}{178}e$ |
| 17 | $[17, 17, -w^{2} + w + 8]$ | $-\frac{1}{8}e^{8} + \frac{33}{8}e^{6} - \frac{387}{8}e^{4} + \frac{1895}{8}e^{2} - \frac{809}{2}$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $\phantom{-}\frac{27}{712}e^{9} - \frac{867}{712}e^{7} + \frac{10121}{712}e^{5} - \frac{51093}{712}e^{3} + \frac{23757}{178}e$ |
| 19 | $[19, 19, -w^{2} + 6]$ | $-\frac{1}{178}e^{9} + \frac{21}{89}e^{7} - \frac{599}{178}e^{5} + \frac{1673}{89}e^{3} - \frac{2986}{89}e$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}\frac{31}{356}e^{9} - \frac{1035}{356}e^{7} + \frac{12517}{356}e^{5} - \frac{64833}{356}e^{3} + \frac{30263}{89}e$ |
| 25 | $[25, 5, w^{2} - 7]$ | $\phantom{-}\frac{1}{178}e^{9} - \frac{21}{89}e^{7} + \frac{599}{178}e^{5} - \frac{1762}{89}e^{3} + \frac{3787}{89}e$ |
| 27 | $[27, 3, -3]$ | $\phantom{-}1$ |
| 31 | $[31, 31, w^{2} - 2w - 8]$ | $\phantom{-}\frac{1}{8}e^{8} - \frac{31}{8}e^{6} + \frac{351}{8}e^{4} - \frac{1741}{8}e^{2} + \frac{807}{2}$ |
| 37 | $[37, 37, w^{2} - 2w - 6]$ | $-\frac{1}{4}e^{8} + \frac{33}{4}e^{6} - \frac{391}{4}e^{4} + \frac{1967}{4}e^{2} - 887$ |
| 41 | $[41, 41, -w - 4]$ | $\phantom{-}\frac{1}{8}e^{8} - \frac{33}{8}e^{6} + \frac{387}{8}e^{4} - \frac{1879}{8}e^{2} + \frac{785}{2}$ |
| 41 | $[41, 41, w^{2} - 2w - 7]$ | $-\frac{1}{4}e^{8} + \frac{17}{2}e^{6} - \frac{421}{4}e^{4} + 559e^{2} - 1062$ |
| 47 | $[47, 47, 2w^{2} - 3w - 7]$ | $\phantom{-}\frac{73}{712}e^{9} - \frac{2443}{712}e^{7} + \frac{29487}{712}e^{5} - \frac{150897}{712}e^{3} + \frac{68227}{178}e$ |
| 53 | $[53, 53, -w^{2} + w + 9]$ | $-\frac{1}{8}e^{8} + \frac{29}{8}e^{6} - \frac{295}{8}e^{4} + \frac{1239}{8}e^{2} - \frac{449}{2}$ |
| 61 | $[61, 61, 3w^{2} - 2w - 17]$ | $-\frac{14}{89}e^{9} + \frac{1907}{356}e^{7} - \frac{5894}{89}e^{5} + \frac{124809}{356}e^{3} - \frac{59222}{89}e$ |
| 67 | $[67, 67, 2w - 1]$ | $\phantom{-}\frac{73}{712}e^{9} - \frac{2621}{712}e^{7} + \frac{33759}{712}e^{5} - \frac{182759}{712}e^{3} + \frac{86561}{178}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $27$ | $[27, 3, -3]$ | $-1$ |