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: | $[12, 6, 2w + 2]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + x^{4} - 11x^{3} - 8x^{2} + 24x + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 6]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 1]$ | $-1$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{4}e^{3} - \frac{11}{4}e^{2} - e + 4$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{4}e^{3} - \frac{7}{4}e^{2} - e$ |
| 11 | $[11, 11, w + 1]$ | $-e^{3} - e^{2} + 6e + 4$ |
| 11 | $[11, 11, w + 10]$ | $-e$ |
| 17 | $[17, 17, -3w + 17]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + \frac{9}{2}e^{2} + e - 6$ |
| 29 | $[29, 29, w + 11]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{4}e^{3} - \frac{7}{4}e^{2} - 4$ |
| 29 | $[29, 29, w + 18]$ | $-\frac{3}{4}e^{4} + \frac{1}{4}e^{3} + \frac{33}{4}e^{2} - 4e - 16$ |
| 37 | $[37, 37, w + 16]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{3}{4}e^{3} - \frac{19}{4}e^{2} + 6e + 12$ |
| 37 | $[37, 37, w + 21]$ | $-\frac{3}{4}e^{4} + \frac{1}{4}e^{3} + \frac{29}{4}e^{2} - 4e - 12$ |
| 47 | $[47, 47, -w - 9]$ | $-2e^{2} + 2e + 12$ |
| 47 | $[47, 47, w - 9]$ | $\phantom{-}e^{2}$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{11}{2}e^{2} + 5e + 10$ |
| 61 | $[61, 61, w + 20]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{4}e^{3} - \frac{7}{4}e^{2}$ |
| 61 | $[61, 61, w + 41]$ | $-\frac{3}{4}e^{4} + \frac{1}{4}e^{3} + \frac{25}{4}e^{2} - 6e - 8$ |
| 89 | $[89, 89, 2w - 15]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + \frac{9}{2}e^{2} + 3e - 10$ |
| 89 | $[89, 89, -2w - 15]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + \frac{9}{2}e^{2} - e - 2$ |
| 103 | $[103, 103, -14w + 81]$ | $\phantom{-}e^{3} + 3e^{2} - 6e - 12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w - 6]$ | $-1$ |
| $3$ | $[3, 3, w + 1]$ | $1$ |