Properties

Label 6.6.1202933.1-49.1-i
Base field 6.6.1202933.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $49$
Level $[49, 49, -w^{5} + w^{4} + 6w^{3} - 3w^{2} - 8w + 2]$
Dimension $14$
CM no
Base change no

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Base field 6.6.1202933.1

Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - 2x^{3} + 6x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[49, 49, -w^{5} + w^{4} + 6w^{3} - 3w^{2} - 8w + 2]$
Dimension: $14$
CM: no
Base change: no
Newspace dimension: $31$

Hecke eigenvalues ($q$-expansion)

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

\(x^{14} - 48x^{12} + 899x^{10} - 8238x^{8} + 37465x^{6} - 72558x^{4} + 29160x^{2} - 1458\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ $\phantom{-}e$
7 $[7, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 4w - 3]$ $\phantom{-}0$
19 $[19, 19, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 4w]$ $-\frac{1978}{375921}e^{13} + \frac{1628}{7371}e^{11} - \frac{1302239}{375921}e^{9} + \frac{3135862}{125307}e^{7} - \frac{2395567}{28917}e^{5} + \frac{1481360}{13923}e^{3} - \frac{132479}{4641}e$
23 $[23, 23, -w^{2} + w + 2]$ $-\frac{2459}{125307}e^{12} + \frac{1927}{2457}e^{10} - \frac{1418407}{125307}e^{8} + \frac{2919113}{41769}e^{6} - \frac{1560401}{9639}e^{4} + \frac{230149}{4641}e^{2} + \frac{4996}{1547}$
25 $[25, 5, w^{5} + w^{4} - 6w^{3} - 7w^{2} + 4w + 2]$ $\phantom{-}\frac{292}{17901}e^{12} - \frac{230}{351}e^{10} + \frac{171167}{17901}e^{8} - \frac{361900}{5967}e^{6} + \frac{210976}{1377}e^{4} - \frac{184352}{1989}e^{2} + \frac{3212}{221}$
41 $[41, 41, 2w^{5} - w^{4} - 10w^{3} + 6w - 1]$ $-\frac{15853}{125307}e^{12} + \frac{12437}{2457}e^{10} - \frac{9189995}{125307}e^{8} + \frac{19134940}{41769}e^{6} - \frac{10660633}{9639}e^{4} + \frac{6946042}{13923}e^{2} - \frac{42446}{1547}$
47 $[47, 47, w^{3} - w^{2} - 4w]$ $\phantom{-}\frac{8093}{125307}e^{12} - \frac{6322}{2457}e^{10} + \frac{4640029}{125307}e^{8} - \frac{9539030}{41769}e^{6} + \frac{5143913}{9639}e^{4} - \frac{2673308}{13923}e^{2} + \frac{5706}{1547}$
53 $[53, 53, w^{5} - 5w^{3} - 3w^{2} + w + 3]$ $-\frac{689}{28917}e^{13} + \frac{535}{567}e^{11} - \frac{388534}{28917}e^{9} + \frac{781604}{9639}e^{7} - \frac{5153903}{28917}e^{5} + \frac{104443}{3213}e^{3} - \frac{626}{357}e$
59 $[59, 59, 2w^{5} - 11w^{3} - 4w^{2} + 8w]$ $\phantom{-}\frac{8093}{125307}e^{12} - \frac{6322}{2457}e^{10} + \frac{4640029}{125307}e^{8} - \frac{9539030}{41769}e^{6} + \frac{5143913}{9639}e^{4} - \frac{2673308}{13923}e^{2} + \frac{2612}{1547}$
61 $[61, 61, w^{2} - 2w - 2]$ $\phantom{-}\frac{1202}{125307}e^{13} - \frac{971}{2457}e^{11} + \frac{752566}{125307}e^{9} - \frac{570208}{13923}e^{7} + \frac{1160597}{9639}e^{5} - \frac{4803653}{41769}e^{3} + \frac{73921}{4641}e$
64 $[64, 2, -2]$ $\phantom{-}\frac{1601}{41769}e^{12} - \frac{139}{91}e^{10} + \frac{919558}{41769}e^{8} - \frac{1898938}{13923}e^{6} + \frac{1039658}{3213}e^{4} - \frac{1874755}{13923}e^{2} + \frac{20567}{1547}$
67 $[67, 67, -w^{4} + 6w^{2} + w - 3]$ $\phantom{-}\frac{146}{3213}e^{13} - \frac{340}{189}e^{11} + \frac{82192}{3213}e^{9} - \frac{493516}{3213}e^{7} + \frac{1058510}{3213}e^{5} - \frac{57104}{3213}e^{3} - \frac{20260}{357}e$
67 $[67, 67, -2w^{4} + w^{3} + 10w^{2} - 6]$ $-\frac{8093}{125307}e^{12} + \frac{6322}{2457}e^{10} - \frac{4640029}{125307}e^{8} + \frac{9539030}{41769}e^{6} - \frac{5143913}{9639}e^{4} + \frac{2673308}{13923}e^{2} + \frac{482}{1547}$
73 $[73, 73, w^{5} - 5w^{3} - 2w^{2} + 2w - 2]$ $-\frac{15388}{375921}e^{13} + \frac{11993}{7371}e^{11} - \frac{8765075}{375921}e^{9} + \frac{17853676}{125307}e^{7} - \frac{9359101}{28917}e^{5} + \frac{3564241}{41769}e^{3} + \frac{60793}{4641}e$
73 $[73, 73, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 2]$ $\phantom{-}\frac{2726}{125307}e^{12} - \frac{2152}{2457}e^{10} + \frac{1612540}{125307}e^{8} - \frac{3464795}{41769}e^{6} + \frac{2096690}{9639}e^{4} - \frac{2049715}{13923}e^{2} + \frac{26008}{1547}$
79 $[79, 79, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 5w - 1]$ $-\frac{12695}{375921}e^{13} + \frac{9832}{7371}e^{11} - \frac{7100500}{375921}e^{9} + \frac{14087600}{125307}e^{7} - \frac{6798224}{28917}e^{5} - \frac{201512}{41769}e^{3} + \frac{215281}{4641}e$
83 $[83, 83, 2w^{5} - 11w^{3} - 4w^{2} + 6w]$ $-\frac{2459}{125307}e^{12} + \frac{1927}{2457}e^{10} - \frac{1418407}{125307}e^{8} + \frac{2919113}{41769}e^{6} - \frac{1560401}{9639}e^{4} + \frac{239431}{4641}e^{2} - \frac{13568}{1547}$
89 $[89, 89, -2w^{5} + 11w^{3} + 4w^{2} - 7w - 2]$ $-\frac{10519}{125307}e^{12} + \frac{8258}{2457}e^{10} - \frac{6110471}{125307}e^{8} + \frac{12759424}{41769}e^{6} - \frac{7158862}{9639}e^{4} + \frac{4843102}{13923}e^{2} - \frac{27088}{1547}$
97 $[97, 97, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 2w - 2]$ $-\frac{2869}{125307}e^{13} + \frac{2204}{2457}e^{11} - \frac{1568054}{125307}e^{9} + \frac{3007000}{41769}e^{7} - \frac{1281520}{9639}e^{5} - \frac{307613}{4641}e^{3} + \frac{224668}{4641}e$
97 $[97, 97, w^{5} - w^{4} - 6w^{3} + 3w^{2} + 7w - 1]$ $-\frac{796}{41769}e^{13} + \frac{635}{819}e^{11} - \frac{483962}{41769}e^{9} + \frac{1074583}{13923}e^{7} - \frac{705562}{3213}e^{5} + \frac{943598}{4641}e^{3} - \frac{187757}{4641}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 4w - 3]$ $1$