Properties

Label 5.5.180769.1-25.3-e
Base field 5.5.180769.1
Weight $[2, 2, 2, 2, 2]$
Level norm $25$
Level $[25, 25, -w^{4} + w^{3} + 4w^{2} - 2w + 1]$
Dimension $14$
CM no
Base change no

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Base field 5.5.180769.1

Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 7x^{2} - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[25, 25, -w^{4} + w^{3} + 4w^{2} - 2w + 1]$
Dimension: $14$
CM: no
Base change: no
Newspace dimension: $34$

Hecke eigenvalues ($q$-expansion)

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

\(x^{14} - 52x^{12} + 980x^{10} - 8607x^{8} + 36791x^{6} - 72842x^{4} + 58464x^{2} - 10368\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w^{4} - 2w^{3} - 4w^{2} + 6w + 1]$ $\phantom{-}\frac{2679391}{1490922144}e^{12} - \frac{33735469}{372730536}e^{10} + \frac{602159051}{372730536}e^{8} - \frac{6417088747}{496974048}e^{6} + \frac{68313677057}{1490922144}e^{4} - \frac{43529172055}{745461072}e^{2} + \frac{146559375}{10353626}$
5 $[5, 5, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $\phantom{-}0$
7 $[7, 7, -w^{4} + 2w^{3} + 4w^{2} - 6w]$ $\phantom{-}e$
7 $[7, 7, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $\phantom{-}\frac{298931}{745461072}e^{12} - \frac{3909197}{186365268}e^{10} + \frac{73668691}{186365268}e^{8} - \frac{844837151}{248487024}e^{6} + \frac{10080573421}{745461072}e^{4} - \frac{7932960323}{372730536}e^{2} + \frac{35234867}{5176813}$
19 $[19, 19, -w^{3} + w^{2} + 4w]$ $-\frac{115335}{165658016}e^{13} + \frac{4407035}{124243512}e^{11} - \frac{80184929}{124243512}e^{9} + \frac{2653515019}{496974048}e^{7} - \frac{3410389321}{165658016}e^{5} + \frac{8631911237}{248487024}e^{3} - \frac{767241283}{31060878}e$
23 $[23, 23, -w^{2} + 3]$ $-\frac{618209}{372730536}e^{12} + \frac{7564217}{93182634}e^{10} - \frac{129723361}{93182634}e^{8} + \frac{1316613149}{124243512}e^{6} - \frac{13081073095}{372730536}e^{4} + \frac{6882779621}{186365268}e^{2} + \frac{6867392}{5176813}$
32 $[32, 2, 2]$ $-\frac{10803653}{1490922144}e^{12} + \frac{133916819}{372730536}e^{10} - \frac{2331500137}{372730536}e^{8} + \frac{23935827017}{496974048}e^{6} - \frac{240903068491}{1490922144}e^{4} + \frac{140917075445}{745461072}e^{2} - \frac{368605001}{10353626}$
37 $[37, 37, -w^{4} + 2w^{3} + 3w^{2} - 7w + 4]$ $-\frac{40173935}{17891065728}e^{13} + \frac{510145409}{4472766432}e^{11} - \frac{9183699235}{4472766432}e^{9} + \frac{98072599835}{5963688576}e^{7} - \frac{1029381845089}{17891065728}e^{5} + \frac{616879537199}{8945532864}e^{3} - \frac{441479907}{41414504}e$
41 $[41, 41, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ $\phantom{-}\frac{19809451}{8945532864}e^{13} - \frac{248310769}{2236383216}e^{11} + \frac{4396412351}{2236383216}e^{9} - \frac{46173621703}{2981844288}e^{7} + \frac{478388943413}{8945532864}e^{5} - \frac{286567379539}{4472766432}e^{3} + \frac{249225165}{20707252}e$
43 $[43, 43, -w^{4} + 2w^{3} + 4w^{2} - 5w - 3]$ $-\frac{8412421}{2236383216}e^{13} + \frac{104605225}{559095804}e^{11} - \frac{1826522729}{559095804}e^{9} + \frac{18742483417}{745461072}e^{7} - \frac{186775932227}{2236383216}e^{5} + \frac{104612633281}{1118191608}e^{3} - \frac{179709080}{15530439}e$
43 $[43, 43, -w^{2} + w + 3]$ $-\frac{45515}{62121756}e^{12} + \frac{573287}{15530439}e^{10} - \frac{10142188}{15530439}e^{8} + \frac{104112583}{20707252}e^{6} - \frac{992484217}{62121756}e^{4} + \frac{466000109}{31060878}e^{2} + \frac{4045964}{5176813}$
47 $[47, 47, 2w^{4} - 3w^{3} - 9w^{2} + 8w + 3]$ $-\frac{31727267}{8945532864}e^{13} + \frac{398603885}{2236383216}e^{11} - \frac{7073784439}{2236383216}e^{9} + \frac{74370384863}{2981844288}e^{7} - \frac{770918640301}{8945532864}e^{5} + \frac{470796697667}{4472766432}e^{3} - \frac{1570369441}{62121756}e$
61 $[61, 61, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 2]$ $\phantom{-}\frac{8776469}{2981844288}e^{13} - \frac{108537527}{745461072}e^{11} + \frac{1879536193}{745461072}e^{9} - \frac{19053599545}{993948096}e^{7} + \frac{185876655595}{2981844288}e^{5} - \frac{99287554013}{1490922144}e^{3} + \frac{614063939}{62121756}e$
79 $[79, 79, w^{2} - w - 5]$ $\phantom{-}\frac{58856995}{8945532864}e^{13} - \frac{739722973}{2236383216}e^{11} + \frac{13137679127}{2236383216}e^{9} - \frac{138353141599}{2981844288}e^{7} + \frac{1438781345837}{8945532864}e^{5} - \frac{877951948291}{4472766432}e^{3} + \frac{2360695561}{62121756}e$
79 $[79, 79, -w^{3} + 2w^{2} + 3w - 3]$ $-\frac{2679391}{1490922144}e^{13} + \frac{33735469}{372730536}e^{11} - \frac{602159051}{372730536}e^{9} + \frac{6417088747}{496974048}e^{7} - \frac{68313677057}{1490922144}e^{5} + \frac{43529172055}{745461072}e^{3} - \frac{136205749}{10353626}e$
79 $[79, 79, -2w^{4} + 4w^{3} + 7w^{2} - 14w + 2]$ $-\frac{7629245}{4472766432}e^{13} + \frac{93409259}{1118191608}e^{11} - \frac{1575489265}{1118191608}e^{9} + \frac{14877739361}{1490922144}e^{7} - \frac{116392114099}{4472766432}e^{5} + \frac{6649501133}{2236383216}e^{3} + \frac{992756821}{31060878}e$
97 $[97, 97, w^{3} - 6w]$ $-\frac{36399917}{5963688576}e^{13} + \frac{451118747}{1490922144}e^{11} - \frac{7832243977}{1490922144}e^{9} + \frac{79493362609}{1987896192}e^{7} - \frac{768840090595}{5963688576}e^{5} + \frac{376374248189}{2981844288}e^{3} + \frac{1306388083}{124243512}e$
101 $[101, 101, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ $-\frac{90746027}{17891065728}e^{13} + \frac{1146523325}{4472766432}e^{11} - \frac{20524640335}{4472766432}e^{9} + \frac{218850419591}{5963688576}e^{7} - \frac{2339277401989}{17891065728}e^{5} + \frac{1565251607099}{8945532864}e^{3} - \frac{6565998289}{124243512}e$
101 $[101, 101, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 1]$ $\phantom{-}\frac{12048223}{2981844288}e^{13} - \frac{150616525}{745461072}e^{11} + \frac{2655320531}{745461072}e^{9} - \frac{27739978187}{993948096}e^{7} + \frac{287585957057}{2981844288}e^{5} - \frac{182810862727}{1490922144}e^{3} + \frac{2384999641}{62121756}e$
107 $[107, 107, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 2]$ $-\frac{5741581}{745461072}e^{12} + \frac{72182635}{186365268}e^{10} - \frac{1278933389}{186365268}e^{8} + \frac{13326653425}{248487024}e^{6} - \frac{134381431139}{745461072}e^{4} + \frac{75408375061}{372730536}e^{2} - \frac{152774149}{5176813}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5,5,w^{4}-w^{3}-5w^{2}+3w+1]$ $-1$