Properties

Label 4.4.17989.1-23.1-c
Base field 4.4.17989.1
Weight $[2, 2, 2, 2]$
Level norm $23$
Level $[23, 23, -w^{3} + w^{2} + 6w + 1]$
Dimension $23$
CM no
Base change no

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Base field 4.4.17989.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - 3x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[23, 23, -w^{3} + w^{2} + 6w + 1]$
Dimension: $23$
CM: no
Base change: no
Newspace dimension: $49$

Hecke eigenvalues ($q$-expansion)

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

\(x^{23} + 5x^{22} - 31x^{21} - 178x^{20} + 369x^{19} + 2612x^{18} - 2106x^{17} - 20750x^{16} + 5590x^{15} + 98183x^{14} - 4239x^{13} - 285798x^{12} - 2009x^{11} + 508661x^{10} - 31853x^{9} - 529752x^{8} + 116268x^{7} + 287604x^{6} - 127130x^{5} - 49304x^{4} + 44672x^{3} - 10962x^{2} + 1049x - 28\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 4w + 1]$ $\phantom{-}e$
5 $[5, 5, w^{3} - 2w^{2} - 6w + 2]$ $...$
11 $[11, 11, w^{3} - 2w^{2} - 4w]$ $...$
13 $[13, 13, w^{2} - 3w - 2]$ $...$
16 $[16, 2, 2]$ $...$
17 $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ $...$
17 $[17, 17, -w^{2} + 2w + 3]$ $...$
23 $[23, 23, -w^{3} + w^{2} + 6w + 1]$ $\phantom{-}1$
27 $[27, 3, -2w^{3} + 3w^{2} + 11w - 1]$ $...$
29 $[29, 29, w^{3} - 2w^{2} - 5w + 4]$ $...$
31 $[31, 31, -w^{3} + 2w^{2} + 6w - 3]$ $...$
31 $[31, 31, -w^{3} + 2w^{2} + 5w + 1]$ $...$
31 $[31, 31, w^{3} - 2w^{2} - 6w]$ $...$
31 $[31, 31, -w^{2} + 2w + 1]$ $...$
37 $[37, 37, w^{3} - w^{2} - 7w - 1]$ $...$
43 $[43, 43, w^{2} - w - 4]$ $...$
71 $[71, 71, w^{3} - 2w^{2} - 6w - 1]$ $...$
71 $[71, 71, 5w^{3} - 8w^{2} - 29w + 3]$ $...$
89 $[89, 89, -2w^{3} + 4w^{2} + 10w - 7]$ $...$
97 $[97, 97, -w^{3} + 2w^{2} + 4w - 4]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$23$ $[23, 23, -w^{3} + w^{2} + 6w + 1]$ $-1$