Base field \(\Q(\sqrt{493}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 123\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3, 3, w]$ |
| Dimension: | $17$ |
| 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:
| \(x^{17} + 9x^{16} + 12x^{15} - 113x^{14} - 358x^{13} + 328x^{12} + 2454x^{11} + 1086x^{10} - 7004x^{9} - 7755x^{8} + 7897x^{7} + 14799x^{6} - 458x^{5} - 10058x^{4} - 3541x^{3} + 1460x^{2} + 880x + 104\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $...$ |
| 11 | $[11, 11, w + 1]$ | $...$ |
| 11 | $[11, 11, w + 9]$ | $...$ |
| 13 | $[13, 13, w - 11]$ | $...$ |
| 13 | $[13, 13, w + 10]$ | $...$ |
| 17 | $[17, 17, w + 8]$ | $...$ |
| 25 | $[25, 5, -5]$ | $...$ |
| 29 | $[29, 29, w + 14]$ | $...$ |
| 31 | $[31, 31, w + 5]$ | $...$ |
| 31 | $[31, 31, w + 25]$ | $...$ |
| 37 | $[37, 37, w + 3]$ | $...$ |
| 37 | $[37, 37, w + 33]$ | $...$ |
| 41 | $[41, 41, w]$ | $...$ |
| 41 | $[41, 41, w + 40]$ | $...$ |
| 49 | $[49, 7, -7]$ | $...$ |
| 53 | $[53, 53, -4w - 43]$ | $...$ |
| 53 | $[53, 53, 4w - 47]$ | $...$ |
| 59 | $[59, 59, -w - 13]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $-1$ |