Base field \(\Q(\sqrt{58}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 58\); narrow class number \(2\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[6,6,w - 8]$ |
Dimension: | $2$ |
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:
\(x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $-\frac{1}{2}e$ |
3 | $[3, 3, w + 1]$ | $-\frac{1}{2}e$ |
3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
7 | $[7, 7, -2w + 15]$ | $-2$ |
7 | $[7, 7, -2w - 15]$ | $-5$ |
11 | $[11, 11, w + 5]$ | $-\frac{1}{2}e$ |
11 | $[11, 11, w + 6]$ | $\phantom{-}e$ |
19 | $[19, 19, w + 1]$ | $-2e$ |
19 | $[19, 19, w + 18]$ | $\phantom{-}e$ |
23 | $[23, 23, w + 9]$ | $\phantom{-}9$ |
23 | $[23, 23, -w + 9]$ | $\phantom{-}0$ |
25 | $[25, 5, 5]$ | $-3$ |
29 | $[29, 29, w]$ | $\phantom{-}e$ |
37 | $[37, 37, w + 13]$ | $\phantom{-}\frac{1}{2}e$ |
37 | $[37, 37, w + 24]$ | $\phantom{-}2e$ |
43 | $[43, 43, w + 12]$ | $\phantom{-}\frac{9}{2}e$ |
43 | $[43, 43, w + 31]$ | $\phantom{-}0$ |
61 | $[61, 61, w + 27]$ | $\phantom{-}2e$ |
61 | $[61, 61, w + 34]$ | $-\frac{11}{2}e$ |
71 | $[71, 71, 12w - 91]$ | $-2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,-w]$ | $\frac{1}{2}e$ |
$3$ | $[3,3,-w + 2]$ | $\frac{1}{2}e$ |