Properties

Label 4.4.14336.1-23.1-a
Base field 4.4.14336.1
Weight $[2, 2, 2, 2]$
Level norm $23$
Level $[23, 23, -w - 3]$
Dimension $6$
CM no
Base change no

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Base field 4.4.14336.1

Generator \(w\), with minimal polynomial \(x^{4} - 8x^{2} + 14\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[23, 23, -w - 3]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $38$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 8x^{4} + 15x^{2} - 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w^{3} + w^{2} + 5w - 6]$ $\phantom{-}e$
7 $[7, 7, w^{3} - w^{2} - 5w + 7]$ $-\frac{1}{2}e^{4} + \frac{5}{2}e^{2} + 2$
7 $[7, 7, -w - 1]$ $\phantom{-}2e$
7 $[7, 7, w - 1]$ $\phantom{-}e^{5} - 7e^{3} + 10e$
17 $[17, 17, w^{2} - w - 5]$ $\phantom{-}\frac{3}{2}e^{5} - \frac{19}{2}e^{3} + 9e$
17 $[17, 17, w^{2} + w - 5]$ $\phantom{-}e^{5} - 8e^{3} + 15e$
23 $[23, 23, -w - 3]$ $-1$
23 $[23, 23, w - 3]$ $-e^{4} + 5e^{2} - 4$
25 $[25, 5, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}e^{5} - 8e^{3} + 15e$
25 $[25, 5, -w^{3} - w^{2} + 4w + 3]$ $-\frac{3}{2}e^{5} + \frac{21}{2}e^{3} - 11e$
41 $[41, 41, w^{3} - 4w - 1]$ $-\frac{1}{2}e^{5} + \frac{5}{2}e^{3} + e$
41 $[41, 41, -w^{3} + 4w - 1]$ $-e^{5} + 8e^{3} - 13e$
71 $[71, 71, -w^{3} + 2w^{2} + 4w - 9]$ $\phantom{-}3e^{5} - 21e^{3} + 26e$
71 $[71, 71, w^{3} + 2w^{2} - 4w - 9]$ $\phantom{-}\frac{5}{2}e^{5} - \frac{41}{2}e^{3} + 32e$
73 $[73, 73, w^{3} - w^{2} - 5w + 3]$ $-\frac{3}{2}e^{4} + \frac{13}{2}e^{2} + 8$
73 $[73, 73, w^{3} + w^{2} - 5w - 3]$ $-\frac{5}{2}e^{4} + \frac{29}{2}e^{2} - 8$
79 $[79, 79, 2w^{2} - 2w - 9]$ $\phantom{-}e^{5} - 11e^{3} + 28e$
79 $[79, 79, -2w^{3} + 8w + 5]$ $-\frac{1}{2}e^{5} + \frac{17}{2}e^{3} - 26e$
81 $[81, 3, -3]$ $\phantom{-}2e^{4} - 12e^{2} + 2$
89 $[89, 89, -w^{3} - 2w^{2} + 6w + 13]$ $-\frac{1}{2}e^{4} + \frac{7}{2}e^{2} - 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$23$ $[23,23,-w-3]$ $1$