Properties

Label 4.4.13676.1-17.1-b
Base field 4.4.13676.1
Weight $[2, 2, 2, 2]$
Level norm $17$
Level $[17, 17, 2w^{3} + w^{2} - 10w - 2]$
Dimension $18$
CM no
Base change no

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Base field 4.4.13676.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[17, 17, 2w^{3} + w^{2} - 10w - 2]$
Dimension: $18$
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:

\(x^{18} - 28x^{16} + 318x^{14} + 3x^{13} - 1890x^{12} - 54x^{11} + 6347x^{10} + 376x^{9} - 12178x^{8} - 1301x^{7} + 12875x^{6} + 2293x^{5} - 6792x^{4} - 1843x^{3} + 1321x^{2} + 506x + 30\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}e$
4 $[4, 2, -w^{2} - w + 3]$ $-\frac{4129133}{27869836}e^{17} + \frac{2059763}{27869836}e^{16} + \frac{113248579}{27869836}e^{15} - \frac{56669377}{27869836}e^{14} - \frac{1250162303}{27869836}e^{13} + \frac{307658689}{13934918}e^{12} + \frac{77630343}{302933}e^{11} - \frac{1691549373}{13934918}e^{10} - \frac{22677230369}{27869836}e^{9} + \frac{10028773667}{27869836}e^{8} + \frac{40150315045}{27869836}e^{7} - \frac{7805725615}{13934918}e^{6} - \frac{37858932993}{27869836}e^{5} + \frac{242242645}{605866}e^{4} + \frac{8635243391}{13934918}e^{3} - \frac{2293850647}{27869836}e^{2} - \frac{756163252}{6967459}e - \frac{144382823}{13934918}$
5 $[5, 5, w^{3} - 5w + 1]$ $-\frac{1276709}{6967459}e^{17} + \frac{2663805}{27869836}e^{16} + \frac{70282827}{13934918}e^{15} - \frac{73994135}{27869836}e^{14} - \frac{389066136}{6967459}e^{13} + \frac{816326963}{27869836}e^{12} + \frac{387046915}{1211732}e^{11} - \frac{4592614705}{27869836}e^{10} - \frac{28193737951}{27869836}e^{9} + \frac{3506498805}{6967459}e^{8} + \frac{49372990281}{27869836}e^{7} - \frac{5655789206}{6967459}e^{6} - \frac{11314029329}{6967459}e^{5} + \frac{737019753}{1211732}e^{4} + \frac{19463163855}{27869836}e^{3} - \frac{4181165175}{27869836}e^{2} - \frac{1537961589}{13934918}e - \frac{49503399}{13934918}$
11 $[11, 11, -w^{3} + 6w - 2]$ $-\frac{2488743}{6967459}e^{17} + \frac{1381360}{6967459}e^{16} + \frac{67979849}{6967459}e^{15} - \frac{38025338}{6967459}e^{14} - \frac{745211946}{6967459}e^{13} + \frac{414098205}{6967459}e^{12} + \frac{182878506}{302933}e^{11} - \frac{2288037177}{6967459}e^{10} - \frac{13072455716}{6967459}e^{9} + \frac{6823252081}{6967459}e^{8} + \frac{22249966762}{6967459}e^{7} - \frac{10685730110}{6967459}e^{6} - \frac{19452698388}{6967459}e^{5} + \frac{335750519}{302933}e^{4} + \frac{7681614854}{6967459}e^{3} - \frac{1809790288}{6967459}e^{2} - \frac{1052263598}{6967459}e - \frac{40169934}{6967459}$
13 $[13, 13, -w^{2} + 4]$ $\phantom{-}\frac{4260485}{6967459}e^{17} - \frac{6448353}{13934918}e^{16} - \frac{117221679}{6967459}e^{15} + \frac{177358959}{13934918}e^{14} + \frac{1297811599}{6967459}e^{13} - \frac{1936813809}{13934918}e^{12} - \frac{646161463}{605866}e^{11} + \frac{10758417379}{13934918}e^{10} + \frac{47211353453}{13934918}e^{9} - \frac{16149501642}{6967459}e^{8} - \frac{83305603985}{13934918}e^{7} + \frac{25500415074}{6967459}e^{6} + \frac{38911413296}{6967459}e^{5} - \frac{1620735165}{605866}e^{4} - \frac{35097083857}{13934918}e^{3} + \frac{8789415807}{13934918}e^{2} + \frac{3047231049}{6967459}e + \frac{188582357}{6967459}$
17 $[17, 17, 2w^{3} + w^{2} - 10w - 2]$ $-1$
37 $[37, 37, w^{3} + w^{2} - 6w - 3]$ $-\frac{6761953}{6967459}e^{17} + \frac{4930238}{6967459}e^{16} + \frac{185752657}{6967459}e^{15} - \frac{135397046}{6967459}e^{14} - \frac{2051799238}{6967459}e^{13} + \frac{1475270670}{6967459}e^{12} + \frac{508970410}{302933}e^{11} - \frac{8169963224}{6967459}e^{10} - \frac{36974686712}{6967459}e^{9} + \frac{24430040723}{6967459}e^{8} + \frac{64604038542}{6967459}e^{7} - \frac{38355253669}{6967459}e^{6} - \frac{59278496716}{6967459}e^{5} + \frac{52462103}{13171}e^{4} + \frac{25882852653}{6967459}e^{3} - \frac{6367699255}{6967459}e^{2} - \frac{4315486457}{6967459}e - \frac{315152068}{6967459}$
37 $[37, 37, -w^{3} + 6w - 4]$ $\phantom{-}\frac{3476697}{6967459}e^{17} - \frac{4991117}{13934918}e^{16} - \frac{95450158}{6967459}e^{15} + \frac{136724375}{13934918}e^{14} + \frac{1054262365}{6967459}e^{13} - \frac{1485299601}{13934918}e^{12} - \frac{523725281}{605866}e^{11} + \frac{8199287967}{13934918}e^{10} + \frac{38221115725}{13934918}e^{9} - \frac{12224866888}{6967459}e^{8} - \frac{67579704655}{13934918}e^{7} + \frac{19163777869}{6967459}e^{6} + \frac{31848100990}{6967459}e^{5} - \frac{1203403375}{605866}e^{4} - \frac{29310213837}{13934918}e^{3} + \frac{6130291779}{13934918}e^{2} + \frac{2654110616}{6967459}e + \frac{231657977}{6967459}$
41 $[41, 41, -w^{3} + 5w - 5]$ $-\frac{8572513}{27869836}e^{17} + \frac{1779120}{6967459}e^{16} + \frac{235997629}{27869836}e^{15} - \frac{48981364}{6967459}e^{14} - \frac{2614817503}{27869836}e^{13} + \frac{2144331677}{27869836}e^{12} + \frac{651553231}{1211732}e^{11} - \frac{11956622343}{27869836}e^{10} - \frac{11912122018}{6967459}e^{9} + \frac{36123510559}{27869836}e^{8} + \frac{42041938015}{13934918}e^{7} - \frac{28839486695}{13934918}e^{6} - \frac{78388522057}{27869836}e^{5} + \frac{1871161319}{1211732}e^{4} + \frac{35368454325}{27869836}e^{3} - \frac{5248804129}{13934918}e^{2} - \frac{3243160827}{13934918}e - \frac{110250246}{6967459}$
43 $[43, 43, w^{3} - 4w + 4]$ $-\frac{12172783}{13934918}e^{17} + \frac{5238920}{6967459}e^{16} + \frac{335392905}{13934918}e^{15} - \frac{143752336}{6967459}e^{14} - \frac{3721081721}{13934918}e^{13} + \frac{3134395945}{13934918}e^{12} + \frac{929360987}{605866}e^{11} - \frac{17390534819}{13934918}e^{10} - \frac{34126960857}{6967459}e^{9} + \frac{52187004161}{13934918}e^{8} + \frac{60705183106}{6967459}e^{7} - \frac{41274259467}{6967459}e^{6} - \frac{114806817233}{13934918}e^{5} + \frac{2644942787}{605866}e^{4} + \frac{52616050097}{13934918}e^{3} - \frac{7385047604}{6967459}e^{2} - \frac{4660387517}{6967459}e - \frac{262110274}{6967459}$
43 $[43, 43, -2w^{3} + 11w - 2]$ $-\frac{6720327}{13934918}e^{17} + \frac{5334723}{13934918}e^{16} + \frac{184260189}{13934918}e^{15} - \frac{146288435}{13934918}e^{14} - \frac{2030146461}{13934918}e^{13} + \frac{795980261}{6967459}e^{12} + \frac{250906466}{302933}e^{11} - \frac{4404936137}{6967459}e^{10} - \frac{36268842225}{13934918}e^{9} + \frac{26371145079}{13934918}e^{8} + \frac{62917743797}{13934918}e^{7} - \frac{20837313022}{6967459}e^{6} - \frac{57288556687}{13934918}e^{5} + \frac{670207532}{302933}e^{4} + \frac{12567252140}{6967459}e^{3} - \frac{7680375233}{13934918}e^{2} - \frac{2205378427}{6967459}e - \frac{93193039}{6967459}$
47 $[47, 47, -2w^{3} - w^{2} + 12w]$ $\phantom{-}\frac{2118057}{13934918}e^{17} + \frac{361672}{6967459}e^{16} - \frac{57765241}{13934918}e^{15} - \frac{9502989}{6967459}e^{14} + \frac{632149383}{13934918}e^{13} + \frac{203631821}{13934918}e^{12} - \frac{154680825}{605866}e^{11} - \frac{1135078485}{13934918}e^{10} + \frac{5497305689}{6967459}e^{9} + \frac{3502391817}{13934918}e^{8} - \frac{9256771641}{6967459}e^{7} - \frac{2984173863}{6967459}e^{6} + \frac{15817034203}{13934918}e^{5} + \frac{228919217}{605866}e^{4} - \frac{5788191961}{13934918}e^{3} - \frac{984058283}{6967459}e^{2} + \frac{257424170}{6967459}e + \frac{96227880}{6967459}$
47 $[47, 47, 2w - 1]$ $-\frac{12141839}{13934918}e^{17} + \frac{20866259}{27869836}e^{16} + \frac{334493635}{13934918}e^{15} - \frac{571544683}{27869836}e^{14} - \frac{3708733589}{13934918}e^{13} + \frac{6216433167}{27869836}e^{12} + \frac{1849480521}{1211732}e^{11} - \frac{34379259069}{27869836}e^{10} - \frac{135319395635}{27869836}e^{9} + \frac{51347333351}{13934918}e^{8} + \frac{238790334743}{27869836}e^{7} - \frac{80653081129}{13934918}e^{6} - \frac{55558206207}{6967459}e^{5} + \frac{5101144147}{1211732}e^{4} + \frac{99079504963}{27869836}e^{3} - \frac{27504532711}{27869836}e^{2} - \frac{8479289619}{13934918}e - \frac{519955599}{13934918}$
61 $[61, 61, -w^{3} + w^{2} + 6w - 5]$ $-\frac{4571397}{13934918}e^{17} + \frac{3355595}{13934918}e^{16} + \frac{125732115}{13934918}e^{15} - \frac{89827839}{13934918}e^{14} - \frac{1392421571}{13934918}e^{13} + \frac{473754260}{6967459}e^{12} + \frac{173690810}{302933}e^{11} - \frac{2513679923}{6967459}e^{10} - \frac{25549988175}{13934918}e^{9} + \frac{14184851675}{13934918}e^{8} + \frac{45804966081}{13934918}e^{7} - \frac{10253306210}{6967459}e^{6} - \frac{44168419505}{13934918}e^{5} + \frac{280739765}{302933}e^{4} + \frac{10469088914}{6967459}e^{3} - \frac{1896909633}{13934918}e^{2} - \frac{1966637924}{6967459}e - \frac{203788321}{6967459}$
71 $[71, 71, w^{3} + w^{2} - 4w - 3]$ $\phantom{-}\frac{32007049}{27869836}e^{17} - \frac{6763131}{6967459}e^{16} - \frac{882105865}{27869836}e^{15} + \frac{185179028}{6967459}e^{14} + \frac{9783397831}{27869836}e^{13} - \frac{8054930261}{27869836}e^{12} - \frac{2439662103}{1211732}e^{11} + \frac{44550179047}{27869836}e^{10} + \frac{44609761146}{6967459}e^{9} - \frac{133130950587}{27869836}e^{8} - \frac{157200813929}{13934918}e^{7} + \frac{104642792777}{13934918}e^{6} + \frac{291109661025}{27869836}e^{5} - \frac{6631548263}{1211732}e^{4} - \frac{127704598085}{27869836}e^{3} + \frac{18053605411}{13934918}e^{2} + \frac{10506677539}{13934918}e + \frac{315556914}{6967459}$
71 $[71, 71, 2w^{3} + 2w^{2} - 9w - 2]$ $-\frac{50416993}{27869836}e^{17} + \frac{7508944}{6967459}e^{16} + \frac{1384088367}{27869836}e^{15} - \frac{412715515}{13934918}e^{14} - \frac{15281811039}{27869836}e^{13} + \frac{8977258681}{27869836}e^{12} + \frac{3790463445}{1211732}e^{11} - \frac{49520396183}{27869836}e^{10} - \frac{137761401039}{13934918}e^{9} + \frac{147240762591}{27869836}e^{8} + \frac{241141401873}{13934918}e^{7} - \frac{57328565113}{6967459}e^{6} - \frac{443832375959}{27869836}e^{5} + \frac{7113329617}{1211732}e^{4} + \frac{193546759781}{27869836}e^{3} - \frac{8998861082}{6967459}e^{2} - \frac{15754228191}{13934918}e - \frac{591623829}{6967459}$
79 $[79, 79, w^{3} + w^{2} - 6w - 5]$ $\phantom{-}\frac{2680835}{13934918}e^{17} - \frac{7232181}{27869836}e^{16} - \frac{36935384}{6967459}e^{15} + \frac{199433479}{27869836}e^{14} + \frac{820729113}{13934918}e^{13} - \frac{2194910905}{27869836}e^{12} - \frac{411817029}{1211732}e^{11} + \frac{12361730243}{27869836}e^{10} + \frac{30585457871}{27869836}e^{9} - \frac{18985847683}{13934918}e^{8} - \frac{55797550973}{27869836}e^{7} + \frac{15623589687}{6967459}e^{6} + \frac{27859822371}{13934918}e^{5} - \frac{2161465023}{1211732}e^{4} - \frac{28420757521}{27869836}e^{3} + \frac{14409403407}{27869836}e^{2} + \frac{2942895219}{13934918}e - \frac{25915913}{13934918}$
81 $[81, 3, -3]$ $-\frac{22151773}{13934918}e^{17} + \frac{7619253}{6967459}e^{16} + \frac{608291023}{13934918}e^{15} - \frac{209281311}{6967459}e^{14} - \frac{6715252643}{13934918}e^{13} + \frac{4557368981}{13934918}e^{12} + \frac{72347383}{26342}e^{11} - \frac{25198578245}{13934918}e^{10} - \frac{60303635811}{6967459}e^{9} + \frac{75163547983}{13934918}e^{8} + \frac{104824379256}{6967459}e^{7} - \frac{58795218658}{6967459}e^{6} - \frac{189995131487}{13934918}e^{5} + \frac{3681970049}{605866}e^{4} + \frac{80459044589}{13934918}e^{3} - \frac{9720587468}{6967459}e^{2} - \frac{6254834700}{6967459}e - \frac{404039600}{6967459}$
83 $[83, 83, -3w^{3} - w^{2} + 16w + 3]$ $\phantom{-}\frac{5957995}{13934918}e^{17} - \frac{12999161}{27869836}e^{16} - \frac{81746728}{6967459}e^{15} + \frac{350418707}{27869836}e^{14} + \frac{1802266059}{13934918}e^{13} - \frac{3750279961}{27869836}e^{12} - \frac{891676289}{1211732}e^{11} + \frac{20399298387}{27869836}e^{10} + \frac{64592112003}{27869836}e^{9} - \frac{29990665847}{13934918}e^{8} - \frac{112725516649}{27869836}e^{7} + \frac{23324647341}{6967459}e^{6} + \frac{52036962765}{13934918}e^{5} - \frac{2980469531}{1211732}e^{4} - \frac{46851455553}{27869836}e^{3} + \frac{17358184475}{27869836}e^{2} + \frac{4223872473}{13934918}e + \frac{161124891}{13934918}$
97 $[97, 97, w^{3} + w^{2} - 6w + 1]$ $\phantom{-}\frac{46371345}{27869836}e^{17} - \frac{8539269}{6967459}e^{16} - \frac{1275142867}{27869836}e^{15} + \frac{468068597}{13934918}e^{14} + \frac{14101745275}{27869836}e^{13} - \frac{10180690205}{27869836}e^{12} - \frac{3502779573}{1211732}e^{11} + \frac{56293908463}{27869836}e^{10} + \frac{127406880543}{13934918}e^{9} - \frac{168268030887}{27869836}e^{8} - \frac{222817245549}{13934918}e^{7} + \frac{66235710124}{6967459}e^{6} + \frac{408465857467}{27869836}e^{5} - \frac{8434200905}{1211732}e^{4} - \frac{177034739249}{27869836}e^{3} + \frac{11656939376}{6967459}e^{2} + \frac{14483432907}{13934918}e + \frac{401019017}{6967459}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, 2w^{3} + w^{2} - 10w - 2]$ $1$