Base field \(\Q(\sqrt{377}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 94\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[8,4,-2w + 2]$ |
Dimension: | $10$ |
CM: | no |
Base change: | no |
Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} + x^{9} - 42x^{8} - 6x^{7} + 594x^{6} - 424x^{5} - 2735x^{4} + 4203x^{3} - 1180x^{2} - 466x + 172\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $-1$ |
2 | $[2, 2, w + 1]$ | $\phantom{-}0$ |
9 | $[9, 3, 3]$ | $\phantom{-}e$ |
11 | $[11, 11, w + 2]$ | $...$ |
11 | $[11, 11, w + 8]$ | $...$ |
13 | $[13, 13, 4w - 41]$ | $...$ |
19 | $[19, 19, w + 7]$ | $...$ |
19 | $[19, 19, w + 11]$ | $...$ |
23 | $[23, 23, -2w + 21]$ | $...$ |
23 | $[23, 23, -2w - 19]$ | $...$ |
25 | $[25, 5, -5]$ | $...$ |
29 | $[29, 29, 6w - 61]$ | $...$ |
31 | $[31, 31, w + 12]$ | $...$ |
31 | $[31, 31, w + 18]$ | $...$ |
37 | $[37, 37, w + 4]$ | $...$ |
37 | $[37, 37, w + 32]$ | $...$ |
41 | $[41, 41, w + 3]$ | $...$ |
41 | $[41, 41, w + 37]$ | $...$ |
47 | $[47, 47, w]$ | $...$ |
47 | $[47, 47, w + 46]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,-w + 1]$ | $-1$ |
$2$ | $[2,2,-w + 2]$ | $1$ |