Properties

Label 6.6.1202933.1-25.1-b
Base field 6.6.1202933.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $25$
Level $[25, 5, w^{5} + w^{4} - 6w^{3} - 7w^{2} + 4w + 2]$
Dimension $11$
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: $[25, 5, w^{5} + w^{4} - 6w^{3} - 7w^{2} + 4w + 2]$
Dimension: $11$
CM: no
Base change: no
Newspace dimension: $19$

Hecke eigenvalues ($q$-expansion)

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

\(x^{11} - 4x^{10} - 36x^{9} + 140x^{8} + 435x^{7} - 1508x^{6} - 2498x^{5} + 6067x^{4} + 7104x^{3} - 6760x^{2} - 7104x - 1120\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ $\phantom{-}e$
7 $[7, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 4w - 3]$ $-\frac{10810673}{455558424}e^{10} + \frac{77929}{18981601}e^{9} + \frac{32786749}{37963202}e^{8} + \frac{4163327}{113889606}e^{7} - \frac{4610823211}{455558424}e^{6} - \frac{83427517}{18981601}e^{5} + \frac{10109489405}{227779212}e^{4} + \frac{15694249613}{455558424}e^{3} - \frac{5915954467}{113889606}e^{2} - \frac{2816553796}{56944803}e - \frac{461520880}{56944803}$
19 $[19, 19, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 4w]$ $\phantom{-}\frac{1386251}{75926404}e^{10} + \frac{260525}{37963202}e^{9} - \frac{12811010}{18981601}e^{8} - \frac{7326688}{18981601}e^{7} + \frac{610740601}{75926404}e^{6} + \frac{281670363}{37963202}e^{5} - \frac{1324218211}{37963202}e^{4} - \frac{3334191331}{75926404}e^{3} + \frac{1324868877}{37963202}e^{2} + \frac{1196049132}{18981601}e + \frac{348587846}{18981601}$
23 $[23, 23, -w^{2} + w + 2]$ $-\frac{35493239}{455558424}e^{10} + \frac{912625}{75926404}e^{9} + \frac{54041503}{18981601}e^{8} + \frac{8206517}{113889606}e^{7} - \frac{15282975829}{455558424}e^{6} - \frac{940977609}{75926404}e^{5} + \frac{33569706305}{227779212}e^{4} + \frac{45615631271}{455558424}e^{3} - \frac{39458122721}{227779212}e^{2} - \frac{17293563425}{113889606}e - \frac{1280257558}{56944803}$
25 $[25, 5, w^{5} + w^{4} - 6w^{3} - 7w^{2} + 4w + 2]$ $-1$
41 $[41, 41, 2w^{5} - w^{4} - 10w^{3} + 6w - 1]$ $-\frac{2741357}{75926404}e^{10} + \frac{488421}{75926404}e^{9} + \frac{24789058}{18981601}e^{8} + \frac{1071862}{18981601}e^{7} - \frac{1153133811}{75926404}e^{6} - \frac{532060953}{75926404}e^{5} + \frac{2510159403}{37963202}e^{4} + \frac{4323217495}{75926404}e^{3} - \frac{5820720409}{75926404}e^{2} - \frac{1714984826}{18981601}e - \frac{224600828}{18981601}$
47 $[47, 47, w^{3} - w^{2} - 4w]$ $-\frac{19372597}{455558424}e^{10} + \frac{2533245}{75926404}e^{9} + \frac{28874738}{18981601}e^{8} - \frac{100272881}{113889606}e^{7} - \frac{7881941639}{455558424}e^{6} + \frac{238182095}{75926404}e^{5} + \frac{16658828131}{227779212}e^{4} + \frac{6502799149}{455558424}e^{3} - \frac{18709187149}{227779212}e^{2} - \frac{3843908413}{113889606}e - \frac{294830756}{56944803}$
53 $[53, 53, w^{5} - 5w^{3} - 3w^{2} + w + 3]$ $-\frac{1197467}{56944803}e^{10} + \frac{330745}{18981601}e^{9} + \frac{14143687}{18981601}e^{8} - \frac{26125318}{56944803}e^{7} - \frac{484631992}{56944803}e^{6} + \frac{29836259}{18981601}e^{5} + \frac{2187845437}{56944803}e^{4} + \frac{435348611}{56944803}e^{3} - \frac{3199110487}{56944803}e^{2} - \frac{1074795122}{56944803}e + \frac{538960444}{56944803}$
59 $[59, 59, 2w^{5} - 11w^{3} - 4w^{2} + 8w]$ $\phantom{-}\frac{3820394}{56944803}e^{10} - \frac{3902517}{75926404}e^{9} - \frac{91650765}{37963202}e^{8} + \frac{79328818}{56944803}e^{7} + \frac{1590930082}{56944803}e^{6} - \frac{424035543}{75926404}e^{5} - \frac{14097571205}{113889606}e^{4} - \frac{2136118657}{113889606}e^{3} + \frac{37141159159}{227779212}e^{2} + \frac{6108529981}{113889606}e - \frac{236934640}{56944803}$
61 $[61, 61, w^{2} - 2w - 2]$ $-\frac{210027}{6602296}e^{10} - \frac{7297}{3301148}e^{9} + \frac{955502}{825287}e^{8} + \frac{584703}{1650574}e^{7} - \frac{89447057}{6602296}e^{6} - \frac{32658707}{3301148}e^{5} + \frac{193748245}{3301148}e^{4} + \frac{435513083}{6602296}e^{3} - \frac{212378957}{3301148}e^{2} - \frac{155365651}{1650574}e - \frac{11809830}{825287}$
64 $[64, 2, -2]$ $\phantom{-}\frac{2069489}{75926404}e^{10} + \frac{739067}{75926404}e^{9} - \frac{19268996}{18981601}e^{8} - \frac{9603757}{18981601}e^{7} + \frac{928073303}{75926404}e^{6} + \frac{719782609}{75926404}e^{5} - \frac{2026604401}{37963202}e^{4} - \frac{4233064175}{75926404}e^{3} + \frac{4076428053}{75926404}e^{2} + \frac{1463979835}{18981601}e + \frac{518314575}{18981601}$
67 $[67, 67, -w^{4} + 6w^{2} + w - 3]$ $-\frac{10282589}{227779212}e^{10} + \frac{2318007}{75926404}e^{9} + \frac{30806881}{18981601}e^{8} - \frac{41944117}{56944803}e^{7} - \frac{4253706115}{227779212}e^{6} + \frac{43692197}{75926404}e^{5} + \frac{9244291511}{113889606}e^{4} + \frac{7012300895}{227779212}e^{3} - \frac{22659106201}{227779212}e^{2} - \frac{3719238923}{56944803}e - \frac{430927022}{56944803}$
67 $[67, 67, -2w^{4} + w^{3} + 10w^{2} - 6]$ $\phantom{-}\frac{1211935}{227779212}e^{10} + \frac{2386593}{37963202}e^{9} - \frac{5005255}{18981601}e^{8} - \frac{125524720}{56944803}e^{7} + \frac{967684445}{227779212}e^{6} + \frac{937128945}{37963202}e^{5} - \frac{2365934911}{113889606}e^{4} - \frac{23772373207}{227779212}e^{3} + \frac{1263884719}{113889606}e^{2} + \frac{7018803136}{56944803}e + \frac{2108931526}{56944803}$
73 $[73, 73, w^{5} - 5w^{3} - 2w^{2} + 2w - 2]$ $\phantom{-}\frac{26764841}{455558424}e^{10} - \frac{231168}{18981601}e^{9} - \frac{81322921}{37963202}e^{8} + \frac{3086053}{113889606}e^{7} + \frac{11449325563}{455558424}e^{6} + \frac{170574156}{18981601}e^{5} - \frac{24961741493}{227779212}e^{4} - \frac{35377764437}{455558424}e^{3} + \frac{14271545227}{113889606}e^{2} + \frac{6944545303}{56944803}e + \frac{1299702694}{56944803}$
73 $[73, 73, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 2]$ $-\frac{30035449}{455558424}e^{10} - \frac{515189}{37963202}e^{9} + \frac{93340799}{37963202}e^{8} + \frac{88795243}{113889606}e^{7} - \frac{13581486755}{455558424}e^{6} - \frac{629350715}{37963202}e^{5} + \frac{30524753965}{227779212}e^{4} + \frac{46884373405}{455558424}e^{3} - \frac{9216735799}{56944803}e^{2} - \frac{8108160734}{56944803}e - \frac{836075846}{56944803}$
79 $[79, 79, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 5w - 1]$ $-\frac{1339275}{75926404}e^{10} + \frac{793407}{75926404}e^{9} + \frac{23577981}{37963202}e^{8} - \frac{5738754}{18981601}e^{7} - \frac{526445517}{75926404}e^{6} + \frac{110494389}{75926404}e^{5} + \frac{545190062}{18981601}e^{4} + \frac{41994905}{75926404}e^{3} - \frac{2589946807}{75926404}e^{2} + \frac{58818911}{37963202}e + \frac{127529206}{18981601}$
83 $[83, 83, 2w^{5} - 11w^{3} - 4w^{2} + 6w]$ $\phantom{-}\frac{554339}{113889606}e^{10} - \frac{1141037}{37963202}e^{9} - \frac{2977344}{18981601}e^{8} + \frac{62306498}{56944803}e^{7} + \frac{188752123}{113889606}e^{6} - \frac{477112711}{37963202}e^{5} - \frac{558275687}{56944803}e^{4} + \frac{6307379335}{113889606}e^{3} + \frac{3689871481}{113889606}e^{2} - \frac{4012327205}{56944803}e - \frac{1587344042}{56944803}$
89 $[89, 89, -2w^{5} + 11w^{3} + 4w^{2} - 7w - 2]$ $\phantom{-}\frac{3467485}{37963202}e^{10} - \frac{38207}{18981601}e^{9} - \frac{63944143}{18981601}e^{8} - \frac{7110098}{18981601}e^{7} + \frac{1526149609}{37963202}e^{6} + \frac{294708073}{18981601}e^{5} - \frac{3374734666}{18981601}e^{4} - \frac{4245476885}{37963202}e^{3} + \frac{3925115654}{18981601}e^{2} + \frac{2989738045}{18981601}e + \frac{643847174}{18981601}$
97 $[97, 97, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 2w - 2]$ $\phantom{-}\frac{4350817}{56944803}e^{10} - \frac{926465}{37963202}e^{9} - \frac{52867450}{18981601}e^{8} + \frac{21971060}{56944803}e^{7} + \frac{1865299757}{56944803}e^{6} + \frac{260521293}{37963202}e^{5} - \frac{8243993342}{56944803}e^{4} - \frac{4251091879}{56944803}e^{3} + \frac{19994675503}{113889606}e^{2} + \frac{6494731852}{56944803}e + \frac{1000696030}{56944803}$
97 $[97, 97, w^{5} - w^{4} - 6w^{3} + 3w^{2} + 7w - 1]$ $\phantom{-}\frac{17963975}{455558424}e^{10} - \frac{318649}{75926404}e^{9} - \frac{27406958}{18981601}e^{8} - \frac{3393485}{113889606}e^{7} + \frac{7791559789}{455558424}e^{6} + \frac{386337925}{75926404}e^{5} - \frac{17272522541}{227779212}e^{4} - \frac{18816004007}{455558424}e^{3} + \frac{21354583745}{227779212}e^{2} + \frac{7114869383}{113889606}e + \frac{442591756}{56944803}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$25$ $[25, 5, w^{5} + w^{4} - 6w^{3} - 7w^{2} + 4w + 2]$ $1$