Base field 4.4.18097.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 6x + 4\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[27, 3, -w^{3} + 7w + 1]$ |
| Dimension: | $33$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $66$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{33} - 17x^{32} + 77x^{31} + 280x^{30} - 3404x^{29} + 4710x^{28} + 46753x^{27} - 168557x^{26} - 217772x^{25} + 1953163x^{24} - 1049731x^{23} - 11771427x^{22} + 19021382x^{21} + 38124905x^{20} - 111704092x^{19} - 46891180x^{18} + 367180134x^{17} - 105158409x^{16} - 741649235x^{15} + 545295624x^{14} + 934967853x^{13} - 1050081353x^{12} - 717536180x^{11} + 1147658028x^{10} + 312002124x^{9} - 765745003x^{8} - 66456453x^{7} + 313547145x^{6} + 7097051x^{5} - 75708648x^{4} - 2305779x^{3} + 9252663x^{2} + 609703x - 312948\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 1]$ | $\phantom{-}e$ |
| 4 | $[4, 2, w]$ | $...$ |
| 4 | $[4, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - 3]$ | $...$ |
| 7 | $[7, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 2]$ | $...$ |
| 13 | $[13, 13, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ | $...$ |
| 17 | $[17, 17, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w]$ | $...$ |
| 27 | $[27, 3, -w^{3} + 7w + 1]$ | $-1$ |
| 31 | $[31, 31, w + 3]$ | $...$ |
| 31 | $[31, 31, -w^{2} + 5]$ | $...$ |
| 37 | $[37, 37, w^{2} - 3]$ | $...$ |
| 41 | $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{3}{2}w - 2]$ | $...$ |
| 47 | $[47, 47, w^{3} - 5w - 3]$ | $...$ |
| 53 | $[53, 53, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w]$ | $...$ |
| 61 | $[61, 61, w^{3} - w^{2} - 5w + 3]$ | $...$ |
| 83 | $[83, 83, w^{3} + w^{2} - 6w - 7]$ | $...$ |
| 83 | $[83, 83, -w^{3} + 5w + 1]$ | $...$ |
| 83 | $[83, 83, 2w - 1]$ | $...$ |
| 83 | $[83, 83, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 2]$ | $...$ |
| 89 | $[89, 89, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w - 2]$ | $...$ |
| 89 | $[89, 89, w^{3} - 5w + 5]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $27$ | $[27, 3, -w^{3} + 7w + 1]$ | $1$ |