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: | yes |
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 | $[2, 2, w - 6]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{7}{2}e^{4} + 13e^{2} - 11$ |
3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 2]$ | $\phantom{-}\frac{1}{4}e^{7} - 3e^{5} + 8e^{3} - 3e$ |
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 | $[11, 11, w + 10]$ | $-e^{7} + 13e^{5} - 43e^{3} + 33e$ |
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 | $[29, 29, w + 18]$ | $\phantom{-}\frac{3}{4}e^{7} - 10e^{5} + 34e^{3} - 25e$ |
37 | $[37, 37, w + 16]$ | $\phantom{-}\frac{5}{4}e^{7} - 16e^{5} + 52e^{3} - 41e$ |
37 | $[37, 37, w + 21]$ | $\phantom{-}\frac{5}{4}e^{7} - 16e^{5} + 52e^{3} - 41e$ |
47 | $[47, 47, -w - 9]$ | $\phantom{-}\frac{1}{2}e^{6} - 6e^{4} + 18e^{2} - 16$ |
47 | $[47, 47, w - 9]$ | $\phantom{-}\frac{1}{2}e^{6} - 6e^{4} + 18e^{2} - 16$ |
49 | $[49, 7, -7]$ | $\phantom{-}e^{6} - 13e^{4} + 43e^{2} - 26$ |
61 | $[61, 61, w + 20]$ | $-\frac{5}{4}e^{7} + 16e^{5} - 52e^{3} + 43e$ |
61 | $[61, 61, w + 41]$ | $-\frac{5}{4}e^{7} + 16e^{5} - 52e^{3} + 43e$ |
89 | $[89, 89, 2w - 15]$ | $-2e^{6} + 25e^{4} - 75e^{2} + 46$ |
89 | $[89, 89, -2w - 15]$ | $-2e^{6} + 25e^{4} - 75e^{2} + 46$ |
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 \((1)\).