Base field \(\Q(\sqrt{34}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 34\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3, 3, w + 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 7x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 6]$ | $\phantom{-}\frac{1}{3}e^{2} + \frac{5}{3}$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{8}{3}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $-\frac{4}{3}e^{3} - \frac{23}{3}e$ |
| 5 | $[5, 5, w + 3]$ | $-\frac{5}{3}e^{3} - \frac{34}{3}e$ |
| 11 | $[11, 11, w + 1]$ | $-\frac{4}{3}e^{3} - \frac{29}{3}e$ |
| 11 | $[11, 11, w + 10]$ | $\phantom{-}\frac{4}{3}e^{3} + \frac{29}{3}e$ |
| 17 | $[17, 17, -3w + 17]$ | $\phantom{-}\frac{2}{3}e^{2} + \frac{1}{3}$ |
| 29 | $[29, 29, w + 11]$ | $-\frac{11}{3}e^{3} - \frac{79}{3}e$ |
| 29 | $[29, 29, w + 18]$ | $\phantom{-}\frac{7}{3}e^{3} + \frac{44}{3}e$ |
| 37 | $[37, 37, w + 16]$ | $\phantom{-}e^{3} + 4e$ |
| 37 | $[37, 37, w + 21]$ | $\phantom{-}2e^{3} + 15e$ |
| 47 | $[47, 47, -w - 9]$ | $\phantom{-}\frac{4}{3}e^{2} + \frac{38}{3}$ |
| 47 | $[47, 47, w - 9]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{10}{3}$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}e^{2} - 4$ |
| 61 | $[61, 61, w + 20]$ | $-e^{3} - e$ |
| 61 | $[61, 61, w + 41]$ | $-\frac{11}{3}e^{3} - \frac{76}{3}e$ |
| 89 | $[89, 89, 2w - 15]$ | $-\frac{4}{3}e^{2} + \frac{1}{3}$ |
| 89 | $[89, 89, -2w - 15]$ | $\phantom{-}\frac{4}{3}e^{2} - \frac{16}{3}$ |
| 103 | $[103, 103, -14w + 81]$ | $\phantom{-}\frac{5}{3}e^{2} + \frac{7}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $-\frac{1}{3}e^{3} - \frac{8}{3}e$ |