Properties

Label 2.8
Level 2
Weight 8
Dimension 1
Nonzero newspaces 1
Newforms 1
Sturm bound 2
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(2))\).

Total New Old
Modular forms 3 1 2
Cusp forms 1 1 0
Eisenstein series 2 0 2

Trace form

\( q - 8q^{2} + 12q^{3} + 64q^{4} - 210q^{5} - 96q^{6} + 1016q^{7} - 512q^{8} - 2043q^{9} + O(q^{10}) \) \( q - 8q^{2} + 12q^{3} + 64q^{4} - 210q^{5} - 96q^{6} + 1016q^{7} - 512q^{8} - 2043q^{9} + 1680q^{10} + 1092q^{11} + 768q^{12} + 1382q^{13} - 8128q^{14} - 2520q^{15} + 4096q^{16} + 14706q^{17} + 16344q^{18} - 39940q^{19} - 13440q^{20} + 12192q^{21} - 8736q^{22} + 68712q^{23} - 6144q^{24} - 34025q^{25} - 11056q^{26} - 50760q^{27} + 65024q^{28} - 102570q^{29} + 20160q^{30} + 227552q^{31} - 32768q^{32} + 13104q^{33} - 117648q^{34} - 213360q^{35} - 130752q^{36} + 160526q^{37} + 319520q^{38} + 16584q^{39} + 107520q^{40} + 10842q^{41} - 97536q^{42} - 630748q^{43} + 69888q^{44} + 429030q^{45} - 549696q^{46} + 472656q^{47} + 49152q^{48} + 208713q^{49} + 272200q^{50} + 176472q^{51} + 88448q^{52} - 1494018q^{53} + 406080q^{54} - 229320q^{55} - 520192q^{56} - 479280q^{57} + 820560q^{58} + 2640660q^{59} - 161280q^{60} + 827702q^{61} - 1820416q^{62} - 2075688q^{63} + 262144q^{64} - 290220q^{65} - 104832q^{66} - 126004q^{67} + 941184q^{68} + 824544q^{69} + 1706880q^{70} - 1414728q^{71} + 1046016q^{72} + 980282q^{73} - 1284208q^{74} - 408300q^{75} - 2556160q^{76} + 1109472q^{77} - 132672q^{78} - 3566800q^{79} - 860160q^{80} + 3858921q^{81} - 86736q^{82} + 5672892q^{83} + 780288q^{84} - 3088260q^{85} + 5045984q^{86} - 1230840q^{87} - 559104q^{88} - 11951190q^{89} - 3432240q^{90} + 1404112q^{91} + 4397568q^{92} + 2730624q^{93} - 3781248q^{94} + 8387400q^{95} - 393216q^{96} + 8682146q^{97} - 1669704q^{98} - 2230956q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2.8.a \(\chi_{2}(1, \cdot)\) 2.8.a.a 1 1