Properties

Label 4.4.13525.1-25.3-g
Base field 4.4.13525.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25,5,-w + 1]$
Dimension $6$
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: $[25,5,-w + 1]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $25$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 18x^{4} + 71x^{2} - 80\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w + 2]$ $-1$
5 $[5, 5, -\frac{3}{5}w^{3} - w^{2} + \frac{26}{5}w + \frac{42}{5}]$ $\phantom{-}0$
9 $[9, 3, \frac{2}{5}w^{3} - \frac{19}{5}w - \frac{3}{5}]$ $-e^{4} + 15e^{2} - 30$
9 $[9, 3, -\frac{1}{5}w^{3} + \frac{2}{5}w + \frac{4}{5}]$ $\phantom{-}e$
11 $[11, 11, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{28}{5}]$ $-\frac{1}{2}e^{5} + 8e^{3} - \frac{37}{2}e$
11 $[11, 11, \frac{1}{5}w^{3} - w^{2} - \frac{7}{5}w + \frac{36}{5}]$ $\phantom{-}e$
16 $[16, 2, 2]$ $\phantom{-}\frac{3}{4}e^{5} - \frac{23}{2}e^{3} + \frac{89}{4}e$
29 $[29, 29, -w]$ $-5$
29 $[29, 29, \frac{1}{5}w^{3} - \frac{12}{5}w + \frac{1}{5}]$ $-\frac{3}{4}e^{5} + \frac{23}{2}e^{3} - \frac{93}{4}e$
41 $[41, 41, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{38}{5}]$ $\phantom{-}\frac{5}{4}e^{5} - \frac{39}{2}e^{3} + \frac{159}{4}e$
41 $[41, 41, -w^{2} + 10]$ $-2e^{4} + 31e^{2} - 67$
41 $[41, 41, \frac{11}{5}w^{3} + 3w^{2} - \frac{102}{5}w - \frac{149}{5}]$ $\phantom{-}2e^{4} - 31e^{2} + 63$
41 $[41, 41, -\frac{1}{5}w^{3} + w^{2} + \frac{7}{5}w - \frac{26}{5}]$ $-\frac{3}{4}e^{5} + \frac{23}{2}e^{3} - \frac{93}{4}e$
49 $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{19}{5}]$ $\phantom{-}\frac{7}{4}e^{5} - \frac{55}{2}e^{3} + \frac{245}{4}e$
49 $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{44}{5}]$ $\phantom{-}4e^{4} - 61e^{2} + 125$
59 $[59, 59, -\frac{4}{5}w^{3} - w^{2} + \frac{33}{5}w + \frac{36}{5}]$ $-\frac{1}{2}e^{5} + 8e^{3} - \frac{41}{2}e$
59 $[59, 59, -2w^{3} - 3w^{2} + 17w + 26]$ $\phantom{-}2e^{4} - 32e^{2} + 70$
61 $[61, 61, -\frac{1}{5}w^{3} + w^{2} + \frac{12}{5}w - \frac{51}{5}]$ $-\frac{1}{4}e^{5} + \frac{9}{2}e^{3} - \frac{63}{4}e$
61 $[61, 61, \frac{4}{5}w^{3} + w^{2} - \frac{28}{5}w - \frac{41}{5}]$ $\phantom{-}\frac{3}{4}e^{5} - \frac{25}{2}e^{3} + \frac{129}{4}e$
71 $[71, 71, \frac{1}{5}w^{3} + w^{2} - \frac{7}{5}w - \frac{49}{5}]$ $-\frac{5}{2}e^{5} + 39e^{3} - \frac{165}{2}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5,5,-\frac{1}{5}w^{3} + \frac{12}{5}w + \frac{9}{5}]$ $-1$