Base field \(\Q(\sqrt{449}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 112\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[5, 5, -116w - 1171]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $101$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} + x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w + 10]$ | $-2e - 1$ |
2 | $[2, 2, w - 11]$ | $\phantom{-}e$ |
5 | $[5, 5, -116w - 1171]$ | $\phantom{-}1$ |
5 | $[5, 5, 116w - 1287]$ | $-2e - 2$ |
7 | $[7, 7, -1002w - 10115]$ | $-2e - 2$ |
7 | $[7, 7, 1002w - 11117]$ | $\phantom{-}2e + 3$ |
9 | $[9, 3, 3]$ | $-2e - 4$ |
11 | $[11, 11, 10w - 111]$ | $\phantom{-}0$ |
11 | $[11, 11, -10w - 101]$ | $\phantom{-}2e - 3$ |
23 | $[23, 23, -32w + 355]$ | $-6e - 3$ |
23 | $[23, 23, 32w + 323]$ | $-4e - 6$ |
41 | $[41, 41, -8w - 81]$ | $-2e - 8$ |
41 | $[41, 41, -8w + 89]$ | $\phantom{-}2e + 8$ |
53 | $[53, 53, 4w - 45]$ | $-8e - 5$ |
53 | $[53, 53, 4w + 41]$ | $-6$ |
59 | $[59, 59, -3892w + 43181]$ | $-2e - 1$ |
59 | $[59, 59, 3892w + 39289]$ | $\phantom{-}6e + 9$ |
61 | $[61, 61, 770w - 8543]$ | $\phantom{-}8e + 5$ |
61 | $[61, 61, -770w - 7773]$ | $\phantom{-}6$ |
67 | $[67, 67, 158w + 1595]$ | $\phantom{-}6e + 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, -116w - 1171]$ | $-1$ |