Base field 3.3.1345.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[23, 23, -w^{2} - w + 3]$ |
| Dimension: | $15$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $47$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{15} - 2x^{14} - 46x^{13} + 89x^{12} + 772x^{11} - 1493x^{10} - 5724x^{9} + 11690x^{8} + 17682x^{7} - 41910x^{6} - 13441x^{5} + 58952x^{4} - 18095x^{3} - 16862x^{2} + 9108x - 810\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $...$ |
| 7 | $[7, 7, w + 3]$ | $...$ |
| 7 | $[7, 7, -w + 2]$ | $...$ |
| 7 | $[7, 7, -w + 1]$ | $...$ |
| 8 | $[8, 2, 2]$ | $...$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $...$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $...$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $-1$ |
| 27 | $[27, 3, 3]$ | $...$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $...$ |
| 31 | $[31, 31, w^{2} - w - 8]$ | $...$ |
| 37 | $[37, 37, -w - 4]$ | $...$ |
| 43 | $[43, 43, 2w^{2} - 4w - 3]$ | $...$ |
| 47 | $[47, 47, w^{2} - 3]$ | $...$ |
| 53 | $[53, 53, 2w^{2} - w - 11]$ | $...$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $...$ |
| 67 | $[67, 67, w^{2} + w - 8]$ | $...$ |
| 71 | $[71, 71, w^{2} + w - 11]$ | $...$ |
| 73 | $[73, 73, -w^{2} + 4w - 2]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, -w^{2} - w + 3]$ | $1$ |