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 | $[97, 97, w^{5} - w^{4} - 6w^{3} + 3w^{2} + 7w - 1]$ | $-\frac{796}{41769}e^{13} + \frac{635}{819}e^{11} - \frac{483962}{41769}e^{9} + \frac{1074583}{13923}e^{7} - \frac{705562}{3213}e^{5} + \frac{943598}{4641}e^{3} - \frac{187757}{4641}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 4w - 3]$ | $1$ |