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Properties

Label 14.10
Level 14
Weight 10
Dimension 16
Nonzero newspaces 2
Newform subspaces 5
Sturm bound 120
Trace bound 1

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 5 \)
Sturm bound: \(120\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(14))\).

Total New Old
Modular forms 60 16 44
Cusp forms 48 16 32
Eisenstein series 12 0 12

Trace form

\( 16q - 32q^{2} - 12q^{3} - 512q^{4} - 3444q^{5} + 12768q^{6} - 1784q^{7} - 8192q^{8} + 41388q^{9} + O(q^{10}) \) \( 16q - 32q^{2} - 12q^{3} - 512q^{4} - 3444q^{5} + 12768q^{6} - 1784q^{7} - 8192q^{8} + 41388q^{9} + 49056q^{10} + 49506q^{11} - 3072q^{12} + 204410q^{13} - 175904q^{14} + 624372q^{15} - 131072q^{16} - 1171470q^{17} - 849120q^{18} + 892100q^{19} + 514560q^{20} - 61728q^{21} + 775488q^{22} - 6884358q^{23} - 466944q^{24} - 2449688q^{25} - 1334944q^{26} + 23712624q^{27} + 3433984q^{28} - 9160380q^{29} - 18072192q^{30} - 12681910q^{31} - 2097152q^{32} + 25482786q^{33} + 23961216q^{34} + 34021092q^{35} + 29153280q^{36} - 84667126q^{37} - 49294432q^{38} + 33234684q^{39} + 12558336q^{40} + 103079556q^{41} + 50046432q^{42} - 106746652q^{43} + 12673536q^{44} - 240131598q^{45} - 41442432q^{46} + 30612630q^{47} + 31064064q^{48} + 189121360q^{49} - 53004704q^{50} - 11940930q^{51} - 37210624q^{52} + 43182078q^{53} - 126894528q^{54} - 42579468q^{55} + 28696576q^{56} + 110895672q^{57} + 94601856q^{58} + 22747920q^{59} + 147515904q^{60} + 196941860q^{61} + 44818496q^{62} - 114794616q^{63} + 268435456q^{64} - 83308512q^{65} - 22186752q^{66} + 270031526q^{67} - 299896320q^{68} - 930360780q^{69} - 590929248q^{70} + 881132616q^{71} - 217374720q^{72} + 723010118q^{73} + 516837248q^{74} - 687736950q^{75} - 418783744q^{76} - 1135851402q^{77} + 1155007488q^{78} + 1119367706q^{79} - 225705984q^{80} - 737784798q^{81} - 1298006784q^{82} + 12360762q^{83} - 1169058816q^{84} - 540605688q^{85} + 245645504q^{86} + 332551368q^{87} + 257310720q^{88} + 61119390q^{89} + 3590538528q^{90} + 1594598498q^{91} + 1484829696q^{92} - 919222998q^{93} - 367048512q^{94} + 1274394246q^{95} - 119537664q^{96} - 4014782740q^{97} - 2968313888q^{98} - 981228444q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(14))\)

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
14.10.a \(\chi_{14}(1, \cdot)\) 14.10.a.a 1 1
14.10.a.b 1
14.10.a.c 2
14.10.c \(\chi_{14}(9, \cdot)\) 14.10.c.a 6 2
14.10.c.b 6

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)