Properties

Label 2.2.492.1-6.1-g
Base field \(\Q(\sqrt{123}) \)
Weight $[2, 2]$
Level norm $6$
Level $[6, 6, w + 3]$
Dimension $2$
CM no
Base change no

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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 $[59, 59, w - 8]$ $\phantom{-}e + 7$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w - 11]$ $1$
$3$ $[3, 3, w]$ $-1$