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: | $[9, 9, -w + 5]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 11x^{4} + 13x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 6]$ | $\phantom{-}2e^{4} + 21e^{2} + 13$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $-e$ |
| 5 | $[5, 5, w + 3]$ | $-e^{5} - 10e^{3} - 3e$ |
| 11 | $[11, 11, w + 1]$ | $-e^{5} - 11e^{3} - 12e$ |
| 11 | $[11, 11, w + 10]$ | $-e$ |
| 17 | $[17, 17, -3w + 17]$ | $\phantom{-}3e^{4} + 31e^{2} + 22$ |
| 29 | $[29, 29, w + 11]$ | $\phantom{-}e^{5} + 10e^{3}$ |
| 29 | $[29, 29, w + 18]$ | $-8e^{5} - 83e^{3} - 52e$ |
| 37 | $[37, 37, w + 16]$ | $\phantom{-}10e^{5} + 103e^{3} + 58e$ |
| 37 | $[37, 37, w + 21]$ | $\phantom{-}e^{5} + 9e^{3} - 4e$ |
| 47 | $[47, 47, -w - 9]$ | $-2e^{4} - 22e^{2} - 16$ |
| 47 | $[47, 47, w - 9]$ | $-10e^{4} - 103e^{2} - 60$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}6e^{4} + 63e^{2} + 34$ |
| 61 | $[61, 61, w + 20]$ | $\phantom{-}9e^{5} + 94e^{3} + 64e$ |
| 61 | $[61, 61, w + 41]$ | $-6e^{5} - 63e^{3} - 42e$ |
| 89 | $[89, 89, 2w - 15]$ | $-5e^{4} - 51e^{2} - 34$ |
| 89 | $[89, 89, -2w - 15]$ | $\phantom{-}14e^{4} + 146e^{2} + 90$ |
| 103 | $[103, 103, -14w + 81]$ | $\phantom{-}7e^{4} + 72e^{2} + 40$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $1$ |