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: | $[1, 1, 1]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 14x^{6} + 56x^{4} + 76x^{2} + 32\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 6]$ | $-\frac{1}{4}e^{6} - \frac{7}{2}e^{4} - 13e^{2} - 11$ |
| 3 | $[3, 3, w + 1]$ | $-e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $-\frac{1}{4}e^{7} - 3e^{5} - 8e^{3} - 3e$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}\frac{1}{4}e^{7} + 3e^{5} + 8e^{3} + 3e$ |
| 11 | $[11, 11, w + 1]$ | $-e^{7} - 13e^{5} - 43e^{3} - 33e$ |
| 11 | $[11, 11, w + 10]$ | $\phantom{-}e^{7} + 13e^{5} + 43e^{3} + 33e$ |
| 17 | $[17, 17, -3w + 17]$ | $-e^{6} - 12e^{4} - 34e^{2} - 22$ |
| 29 | $[29, 29, w + 11]$ | $\phantom{-}\frac{3}{4}e^{7} + 10e^{5} + 34e^{3} + 25e$ |
| 29 | $[29, 29, w + 18]$ | $-\frac{3}{4}e^{7} - 10e^{5} - 34e^{3} - 25e$ |
| 37 | $[37, 37, w + 16]$ | $-\frac{5}{4}e^{7} - 16e^{5} - 52e^{3} - 41e$ |
| 37 | $[37, 37, w + 21]$ | $\phantom{-}\frac{5}{4}e^{7} + 16e^{5} + 52e^{3} + 41e$ |
| 47 | $[47, 47, -w - 9]$ | $-\frac{1}{2}e^{6} - 6e^{4} - 18e^{2} - 16$ |
| 47 | $[47, 47, w - 9]$ | $-\frac{1}{2}e^{6} - 6e^{4} - 18e^{2} - 16$ |
| 49 | $[49, 7, -7]$ | $-e^{6} - 13e^{4} - 43e^{2} - 26$ |
| 61 | $[61, 61, w + 20]$ | $-\frac{5}{4}e^{7} - 16e^{5} - 52e^{3} - 43e$ |
| 61 | $[61, 61, w + 41]$ | $\phantom{-}\frac{5}{4}e^{7} + 16e^{5} + 52e^{3} + 43e$ |
| 89 | $[89, 89, 2w - 15]$ | $\phantom{-}2e^{6} + 25e^{4} + 75e^{2} + 46$ |
| 89 | $[89, 89, -2w - 15]$ | $\phantom{-}2e^{6} + 25e^{4} + 75e^{2} + 46$ |
| 103 | $[103, 103, -14w + 81]$ | $\phantom{-}3e^{6} + 40e^{4} + 138e^{2} + 104$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).