Base field 5.5.70601.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 2x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[27, 3, w^{4} - w^{3} - 4w^{2} + 2w - 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 5x^{5} - 12x^{4} + 65x^{3} - 42x^{2} - 15x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{4} - 6w^{2} - 2w + 4]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{4} + w^{3} + 5w^{2} - w - 4]$ | $-\frac{1}{5}e^{4} + \frac{4}{5}e^{3} + 3e^{2} - \frac{46}{5}e + \frac{11}{5}$ |
| 11 | $[11, 11, -2w^{4} + w^{3} + 10w^{2} + w - 3]$ | $\phantom{-}\frac{1}{5}e^{5} - \frac{4}{5}e^{4} - 3e^{3} + \frac{46}{5}e^{2} - \frac{11}{5}e + 2$ |
| 11 | $[11, 11, w^{4} - 6w^{2} - 3w + 3]$ | $-\frac{8}{25}e^{5} + \frac{41}{25}e^{4} + \frac{94}{25}e^{3} - \frac{538}{25}e^{2} + \frac{372}{25}e + \frac{86}{25}$ |
| 17 | $[17, 17, w^{2} - 2]$ | $-\frac{9}{25}e^{5} + \frac{38}{25}e^{4} + \frac{132}{25}e^{3} - \frac{474}{25}e^{2} + \frac{126}{25}e + \frac{108}{25}$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w]$ | $\phantom{-}\frac{1}{5}e^{4} - \frac{4}{5}e^{3} - 3e^{2} + \frac{46}{5}e + \frac{9}{5}$ |
| 27 | $[27, 3, w^{4} - w^{3} - 4w^{2} + 2w - 1]$ | $\phantom{-}1$ |
| 29 | $[29, 29, 2w^{4} - 2w^{3} - 9w^{2} + 2w + 3]$ | $\phantom{-}\frac{8}{25}e^{5} - \frac{41}{25}e^{4} - \frac{94}{25}e^{3} + \frac{538}{25}e^{2} - \frac{322}{25}e - \frac{61}{25}$ |
| 32 | $[32, 2, -2]$ | $-\frac{4}{25}e^{5} + \frac{23}{25}e^{4} + \frac{37}{25}e^{3} - \frac{319}{25}e^{2} + \frac{326}{25}e + \frac{103}{25}$ |
| 47 | $[47, 47, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $\phantom{-}\frac{14}{25}e^{5} - \frac{73}{25}e^{4} - \frac{147}{25}e^{3} + \frac{929}{25}e^{2} - \frac{871}{25}e - \frac{43}{25}$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w - 1]$ | $\phantom{-}\frac{1}{5}e^{5} - \frac{3}{5}e^{4} - \frac{19}{5}e^{3} + \frac{31}{5}e^{2} + 9e - \frac{1}{5}$ |
| 53 | $[53, 53, -w^{4} + 7w^{2} - 3]$ | $\phantom{-}\frac{16}{25}e^{5} - \frac{82}{25}e^{4} - \frac{188}{25}e^{3} + \frac{1076}{25}e^{2} - \frac{694}{25}e - \frac{122}{25}$ |
| 53 | $[53, 53, 2w^{4} - 2w^{3} - 9w^{2} + 2w + 2]$ | $\phantom{-}\frac{1}{5}e^{5} - e^{4} - \frac{11}{5}e^{3} + \frac{61}{5}e^{2} - \frac{62}{5}e + \frac{21}{5}$ |
| 53 | $[53, 53, 3w^{4} - 2w^{3} - 16w^{2} + 8]$ | $\phantom{-}\frac{1}{5}e^{5} - \frac{6}{5}e^{4} - \frac{7}{5}e^{3} + \frac{81}{5}e^{2} - \frac{103}{5}e - \frac{28}{5}$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + 4w - 3]$ | $\phantom{-}\frac{21}{25}e^{5} - \frac{107}{25}e^{4} - \frac{243}{25}e^{3} + \frac{1381}{25}e^{2} - \frac{979}{25}e - \frac{217}{25}$ |
| 73 | $[73, 73, 2w^{4} - 12w^{2} - 4w + 5]$ | $-\frac{21}{25}e^{5} + \frac{97}{25}e^{4} + \frac{283}{25}e^{3} - \frac{1231}{25}e^{2} + \frac{469}{25}e + \frac{277}{25}$ |
| 83 | $[83, 83, w^{4} - 5w^{2} - 3w + 3]$ | $-\frac{11}{25}e^{5} + \frac{62}{25}e^{4} + \frac{113}{25}e^{3} - \frac{821}{25}e^{2} + \frac{589}{25}e + \frac{247}{25}$ |
| 97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $\phantom{-}\frac{19}{25}e^{5} - \frac{98}{25}e^{4} - \frac{227}{25}e^{3} + \frac{1284}{25}e^{2} - \frac{731}{25}e - \frac{288}{25}$ |
| 103 | $[103, 103, 2w^{3} - 3w^{2} - 7w + 3]$ | $-\frac{11}{25}e^{5} + \frac{52}{25}e^{4} + \frac{153}{25}e^{3} - \frac{696}{25}e^{2} + \frac{129}{25}e + \frac{332}{25}$ |
| 109 | $[109, 109, -3w^{4} + 2w^{3} + 14w^{2} + w - 6]$ | $\phantom{-}\frac{39}{25}e^{5} - \frac{188}{25}e^{4} - \frac{487}{25}e^{3} + \frac{2404}{25}e^{2} - \frac{1461}{25}e - \frac{428}{25}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $27$ | $[27, 3, w^{4} - w^{3} - 4w^{2} + 2w - 1]$ | $-1$ |