Properties

Label 15.8
Level 15
Weight 8
Dimension 36
Nonzero newspaces 3
Newforms 5
Sturm bound 128
Trace bound 1

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 5 \)
Sturm bound: \(128\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(15))\).

Total New Old
Modular forms 64 44 20
Cusp forms 48 36 12
Eisenstein series 16 8 8

Trace form

\( 36q - 28q^{2} + 78q^{3} - 200q^{4} - 444q^{5} + 1356q^{6} + 3608q^{7} - 2436q^{8} - 2916q^{9} + O(q^{10}) \) \( 36q - 28q^{2} + 78q^{3} - 200q^{4} - 444q^{5} + 1356q^{6} + 3608q^{7} - 2436q^{8} - 2916q^{9} - 4616q^{10} + 7952q^{11} + 8340q^{12} + 5360q^{13} - 34488q^{14} + 26814q^{15} + 38000q^{16} - 32032q^{17} - 126972q^{18} - 64176q^{19} + 46444q^{20} + 134904q^{21} + 146376q^{22} + 170088q^{23} - 237168q^{24} - 85644q^{25} - 445816q^{26} - 224802q^{27} + 436280q^{28} + 717688q^{29} + 774336q^{30} + 71568q^{31} - 1063916q^{32} - 774984q^{33} + 238760q^{34} + 636520q^{35} + 569016q^{36} - 789232q^{37} - 769432q^{38} - 1224396q^{39} - 2054392q^{40} + 883240q^{41} + 1622112q^{42} + 976328q^{43} + 537976q^{44} + 893916q^{45} + 4371848q^{46} + 1210520q^{47} + 1149684q^{48} - 2687956q^{49} - 5555236q^{50} - 4088820q^{51} - 8572528q^{52} + 1575488q^{53} - 393660q^{54} + 7062576q^{55} + 6479040q^{56} + 5320296q^{57} - 1200264q^{58} - 1197184q^{59} + 6515256q^{60} + 1179144q^{61} + 5573928q^{62} - 323496q^{63} + 9724488q^{64} - 3366592q^{65} - 30638208q^{66} - 21756808q^{67} - 9434504q^{68} - 5890968q^{69} - 1513560q^{70} - 4007216q^{71} + 34470036q^{72} + 6676736q^{73} + 20919712q^{74} + 19838094q^{75} + 37710128q^{76} + 6733248q^{77} - 10796952q^{78} - 10874880q^{79} - 39917876q^{80} - 24912684q^{81} - 40630392q^{82} - 17321256q^{83} - 43954272q^{84} - 33002768q^{85} - 6212848q^{86} + 50204484q^{87} + 97866504q^{88} + 58210824q^{89} + 80324424q^{90} + 88309648q^{91} + 15479424q^{92} - 54464928q^{93} - 78524776q^{94} - 33956656q^{95} - 104433168q^{96} - 63625168q^{97} - 21248492q^{98} - 9879408q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(15))\)

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
15.8.a \(\chi_{15}(1, \cdot)\) 15.8.a.a 1 1
15.8.a.b 1
15.8.a.c 2
15.8.b \(\chi_{15}(4, \cdot)\) 15.8.b.a 8 1
15.8.e \(\chi_{15}(2, \cdot)\) 15.8.e.a 24 2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(15)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)