Properties

Label 4.4.11661.1-23.1-f
Base field 4.4.11661.1
Weight $[2, 2, 2, 2]$
Level norm $23$
Level $[23, 23, -w^{3} + 4w + 1]$
Dimension $2$
CM no
Base change no

Related objects

Downloads

Learn more about

Base field 4.4.11661.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 3\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[23, 23, -w^{3} + 4w + 1]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $30$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{2} - 8x - 12\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-2$
3 $[3, 3, w - 2]$ $\phantom{-}0$
3 $[3, 3, w - 1]$ $\phantom{-}2$
16 $[16, 2, 2]$ $\phantom{-}1$
23 $[23, 23, -w^{3} + 4w + 1]$ $-1$
25 $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ $-e$
25 $[25, 5, w^{3} - w^{2} - 3w + 1]$ $\phantom{-}e$
29 $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ $\phantom{-}e - 2$
29 $[29, 29, w^{3} - w^{2} - 5w + 1]$ $-e + 2$
43 $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ $-2e + 8$
43 $[43, 43, w^{3} - w^{2} - 4w + 2]$ $-2e + 8$
61 $[61, 61, -w^{2} + 2w + 4]$ $-e + 4$
61 $[61, 61, w^{2} - 5]$ $\phantom{-}e - 4$
79 $[79, 79, 3w^{3} - 7w^{2} - 8w + 16]$ $\phantom{-}2e - 2$
79 $[79, 79, -w^{3} + w^{2} + 6w - 4]$ $-2e + 2$
101 $[101, 101, -w^{3} + 3w^{2} + w - 7]$ $\phantom{-}e - 8$
101 $[101, 101, w^{3} - 4w - 4]$ $-e + 8$
103 $[103, 103, 2w^{3} - w^{2} - 8w - 1]$ $\phantom{-}2e - 12$
103 $[103, 103, 2w^{3} - 5w^{2} - 4w + 8]$ $\phantom{-}2e - 12$
107 $[107, 107, 2w^{2} - 3w - 4]$ $-2e + 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$23$ $[23, 23, -w^{3} + 4w + 1]$ $1$