Base field \(\Q(\sqrt{123}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 123\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[6, 6, w + 3]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $92$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 2x - 12\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w - 11]$ | $-1$ |
3 | $[3, 3, w]$ | $\phantom{-}1$ |
7 | $[7, 7, w + 2]$ | $-1$ |
7 | $[7, 7, w + 5]$ | $\phantom{-}e$ |
17 | $[17, 17, w + 2]$ | $-\frac{1}{2}e + 1$ |
17 | $[17, 17, w + 15]$ | $\phantom{-}\frac{3}{2}e$ |
19 | $[19, 19, w + 3]$ | $-\frac{1}{2}e - 3$ |
19 | $[19, 19, w + 16]$ | $-e + 1$ |
23 | $[23, 23, -w - 10]$ | $-3$ |
23 | $[23, 23, w - 10]$ | $-\frac{1}{2}e + 4$ |
25 | $[25, 5, -5]$ | $-1$ |
29 | $[29, 29, w + 6]$ | $-e - 4$ |
29 | $[29, 29, w + 23]$ | $-\frac{3}{2}e$ |
37 | $[37, 37, 9w + 100]$ | $\phantom{-}2e - 5$ |
37 | $[37, 37, -2w - 23]$ | $\phantom{-}2$ |
41 | $[41, 41, w]$ | $\phantom{-}e - 5$ |
53 | $[53, 53, w + 21]$ | $-9$ |
53 | $[53, 53, w + 32]$ | $\phantom{-}e - 8$ |
59 | $[59, 59, -w - 8]$ | $-\frac{3}{2}e + 3$ |
59 | $[59, 59, w - 8]$ | $\phantom{-}e + 7$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w - 11]$ | $1$ |
$3$ | $[3, 3, w]$ | $-1$ |