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Properties

Label 8.26
Level 8
Weight 26
Dimension 30
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 104
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 26 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(104\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_1(8))\).

Total New Old
Modular forms 53 32 21
Cusp forms 47 30 17
Eisenstein series 6 2 4

Trace form

\( 30 q - 4050 q^{2} + 1149080 q^{3} + 52495188 q^{4} + 211515876 q^{5} - 6687333812 q^{6} + 20809484400 q^{7} + 38034592200 q^{8} - 5962125663946 q^{9} + O(q^{10}) \) \( 30 q - 4050 q^{2} + 1149080 q^{3} + 52495188 q^{4} + 211515876 q^{5} - 6687333812 q^{6} + 20809484400 q^{7} + 38034592200 q^{8} - 5962125663946 q^{9} - 3802288651368 q^{10} + 15485635681992 q^{11} - 57092744235800 q^{12} + 103066025610900 q^{13} + 161533138906224 q^{14} - 141877876770096 q^{15} - 416206362542832 q^{16} - 99893701762020 q^{17} + 8774518024977410 q^{18} - 13334010647668488 q^{19} - 3644272787238576 q^{20} + 12909334978028736 q^{21} + 67768015991720700 q^{22} - 25588242677922480 q^{23} + 457243516087844240 q^{24} - 482990011657467918 q^{25} - 876642676379768376 q^{26} - 719761167973300240 q^{27} - 1240387130855545440 q^{28} - 1237513611146625036 q^{29} + 8737038823208911472 q^{30} - 3805070149927984704 q^{31} + 24553237779142855200 q^{32} + 5488495175630197760 q^{33} - 67563260959012243140 q^{34} + 22647997795248742176 q^{35} - 94235170606861357620 q^{36} - 12749325069650653020 q^{37} + 97817246778929769900 q^{38} + 114446999226599338512 q^{39} + 130190589030589772832 q^{40} - 34670669754995995284 q^{41} - 221767462932711865760 q^{42} - 27884323355507865720 q^{43} + 371682293442873429384 q^{44} + 72306053395496448532 q^{45} - 619639296664525565616 q^{46} - 2297954322478348956000 q^{47} - 2706903740378932892640 q^{48} + 2915531054426066154030 q^{49} + 4108405079365893722502 q^{50} + 409602981819789776560 q^{51} + 10817960513488638270960 q^{52} - 7279331011896948519420 q^{53} - 13599430808221994674696 q^{54} + 15868822344945341062896 q^{55} + 3532816681983406407744 q^{56} - 8865510898448811503040 q^{57} - 23544937988902132380120 q^{58} + 40052336936347599525864 q^{59} - 45476484210207879194208 q^{60} - 44191960942546065406284 q^{61} + 27985625026734080848320 q^{62} + 144006640177106794143280 q^{63} + 45810979002235348170816 q^{64} - 89700706789722678323592 q^{65} - 100486203994420061935464 q^{66} + 145034109477709735850520 q^{67} - 161016137225230482771480 q^{68} - 369674870067921242309056 q^{69} + 95592117080338301998272 q^{70} + 632960498478939165758448 q^{71} - 84767662758832850164360 q^{72} - 625572837586033893254100 q^{73} + 209235841548412291991640 q^{74} + 1374264371754966962998120 q^{75} + 99120720670626592312872 q^{76} - 1772445516646110900857280 q^{77} - 1326632050446319036711600 q^{78} + 3536883747066398044901472 q^{79} - 2758279558214084387843520 q^{80} - 1546938581803160244575730 q^{81} + 803058427028182556556300 q^{82} + 3301436033609841354601080 q^{83} + 380786770058521170535744 q^{84} - 6399950688455182969926648 q^{85} - 469225350145575223674948 q^{86} + 10744190735086002546088080 q^{87} + 2455220727121995324016080 q^{88} - 2325581437488654888867060 q^{89} - 8684203180274574378076120 q^{90} + 6338610438632050028315808 q^{91} - 3889983295170647973361440 q^{92} - 1203807257622600762133760 q^{93} + 5438699977686463847999136 q^{94} - 21035498842742030718274800 q^{95} + 15221006072562730913222720 q^{96} + 12160169046916136809535100 q^{97} + 2110533914146170008879550 q^{98} - 10814868839908776757628120 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_1(8))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
8.26.a \(\chi_{8}(1, \cdot)\) 8.26.a.a 3 1
8.26.a.b 3
8.26.b \(\chi_{8}(5, \cdot)\) 8.26.b.a 24 1

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)