Base field 3.3.1825.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[27, 3, 3]$ |
| Dimension: | $44$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $80$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{44} - 175x^{42} + 14044x^{40} - 685465x^{38} + 22754037x^{36} - 544203257x^{34} + 9691911961x^{32} - 131009258483x^{30} + 1357773344244x^{28} - 10826860581052x^{26} + 66298949519403x^{24} - 309714958624266x^{22} + 1091739725260030x^{20} - 2861283915217496x^{18} + 5476432463757668x^{16} - 7498263625053694x^{14} + 7165052615816404x^{12} - 4624372634468560x^{10} + 1922341290613056x^{8} - 478921395670272x^{6} + 64186841255936x^{4} - 3992329322496x^{2} + 85642444800\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w + 2]$ | $...$ |
| 7 | $[7, 7, w]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $...$ |
| 11 | $[11, 11, w + 2]$ | $...$ |
| 13 | $[13, 13, w + 1]$ | $...$ |
| 17 | $[17, 17, -w^{2} - w + 4]$ | $...$ |
| 23 | $[23, 23, -w^{2} + 6]$ | $...$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $...$ |
| 23 | $[23, 23, -w + 4]$ | $...$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}1$ |
| 29 | $[29, 29, -w^{2} - 2w + 4]$ | $...$ |
| 31 | $[31, 31, w^{2} - 10]$ | $...$ |
| 41 | $[41, 41, w + 4]$ | $...$ |
| 41 | $[41, 41, w^{2} - 5]$ | $...$ |
| 41 | $[41, 41, -2w - 5]$ | $...$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $...$ |
| 47 | $[47, 47, w^{2} - w - 9]$ | $...$ |
| 49 | $[49, 7, w^{2} - w - 8]$ | $...$ |
| 53 | $[53, 53, 2w^{2} + w - 12]$ | $...$ |
| 59 | $[59, 59, w^{2} - 3]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $27$ | $[27, 3, 3]$ | $-1$ |