Base field 3.3.940.1
Generator \(w\), with minimal polynomial \(x^3 - 7 x - 4\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[27, 3, 3]$ |
| Dimension: | $28$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $52$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{28} - 5 x^{27} - 33 x^{26} + 199 x^{25} + 411 x^{24} - 3429 x^{23} - 1864 x^{22} + 33480 x^{21} - 7836 x^{20} - 203339 x^{19} + 148013 x^{18} + 792060 x^{17} - 874530 x^{16} - 1958770 x^{15} + 2866980 x^{14} + 2894503 x^{13} - 5642985 x^{12} - 2102373 x^{11} + 6590334 x^{10} + 18177 x^9 - 4260937 x^8 + 948849 x^7 + 1298782 x^6 - 479739 x^5 - 111372 x^4 + 59131 x^3 - 3076 x^2 - 536 x + 32\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -w - 1]$ | $...$ |
| 5 | $[5, 5, -w^2 + w + 7]$ | $...$ |
| 5 | $[5, 5, -w^2 + w + 5]$ | $...$ |
| 17 | $[17, 17, -w^2 + 3 w + 1]$ | $...$ |
| 23 | $[23, 23, -w^2 + w + 3]$ | $...$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}1$ |
| 29 | $[29, 29, -w^2 + 3 w - 1]$ | $...$ |
| 37 | $[37, 37, w^2 + w + 1]$ | $...$ |
| 41 | $[41, 41, w^2 - w - 9]$ | $...$ |
| 43 | $[43, 43, -3 w^2 + 3 w + 17]$ | $...$ |
| 47 | $[47, 47, 2 w^2 - 2 w - 13]$ | $...$ |
| 47 | $[47, 47, -2 w + 5]$ | $...$ |
| 53 | $[53, 53, 3 w^2 - w - 19]$ | $...$ |
| 59 | $[59, 59, 2 w - 1]$ | $...$ |
| 67 | $[67, 67, w^2 + w - 5]$ | $...$ |
| 71 | $[71, 71, -3 w^2 + w + 21]$ | $...$ |
| 79 | $[79, 79, 3 w^2 - w - 23]$ | $...$ |
| 89 | $[89, 89, 2 w^2 - 4 w - 7]$ | $...$ |
| 89 | $[89, 89, -2 w^2 - 2 w + 5]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $27$ | $[27, 3, 3]$ | $-1$ |