Properties

Label 4.4.13525.1-29.2-b
Base field 4.4.13525.1
Weight $[2, 2, 2, 2]$
Level norm $29$
Level $[29,29,-\frac{1}{5}w^{3} + \frac{12}{5}w - \frac{1}{5}]$
Dimension $23$
CM no
Base change no

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Base field 4.4.13525.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 12x^{2} + 8x + 29\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[29,29,-\frac{1}{5}w^{3} + \frac{12}{5}w - \frac{1}{5}]$
Dimension: $23$
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:

\(x^{23} - 8x^{22} - 51x^{21} + 540x^{20} + 795x^{19} - 15412x^{18} + 2940x^{17} + 241124x^{16} - 258170x^{15} - 2234339x^{14} + 3768584x^{13} + 12251905x^{12} - 27972050x^{11} - 36211037x^{10} + 117322470x^{9} + 35026916x^{8} - 270558897x^{7} + 83316628x^{6} + 294415889x^{5} - 228054079x^{4} - 73446214x^{3} + 140002919x^{2} - 54272792x + 6881453\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w + 2]$ $\phantom{-}e$
5 $[5, 5, -\frac{3}{5}w^{3} - w^{2} + \frac{26}{5}w + \frac{42}{5}]$ $...$
9 $[9, 3, \frac{2}{5}w^{3} - \frac{19}{5}w - \frac{3}{5}]$ $...$
9 $[9, 3, -\frac{1}{5}w^{3} + \frac{2}{5}w + \frac{4}{5}]$ $...$
11 $[11, 11, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{28}{5}]$ $...$
11 $[11, 11, \frac{1}{5}w^{3} - w^{2} - \frac{7}{5}w + \frac{36}{5}]$ $...$
16 $[16, 2, 2]$ $...$
29 $[29, 29, -w]$ $...$
29 $[29, 29, \frac{1}{5}w^{3} - \frac{12}{5}w + \frac{1}{5}]$ $-1$
41 $[41, 41, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{38}{5}]$ $...$
41 $[41, 41, -w^{2} + 10]$ $...$
41 $[41, 41, \frac{11}{5}w^{3} + 3w^{2} - \frac{102}{5}w - \frac{149}{5}]$ $...$
41 $[41, 41, -\frac{1}{5}w^{3} + w^{2} + \frac{7}{5}w - \frac{26}{5}]$ $...$
49 $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{19}{5}]$ $...$
49 $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{44}{5}]$ $...$
59 $[59, 59, -\frac{4}{5}w^{3} - w^{2} + \frac{33}{5}w + \frac{36}{5}]$ $...$
59 $[59, 59, -2w^{3} - 3w^{2} + 17w + 26]$ $...$
61 $[61, 61, -\frac{1}{5}w^{3} + w^{2} + \frac{12}{5}w - \frac{51}{5}]$ $...$
61 $[61, 61, \frac{4}{5}w^{3} + w^{2} - \frac{28}{5}w - \frac{41}{5}]$ $...$
71 $[71, 71, \frac{1}{5}w^{3} + w^{2} - \frac{7}{5}w - \frac{49}{5}]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29,29,-\frac{1}{5}w^{3} + \frac{12}{5}w - \frac{1}{5}]$ $1$