Properties

Label 15.6
Level 15
Weight 6
Dimension 24
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 96
Trace bound 2

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(96\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(15))\).

Total New Old
Modular forms 48 32 16
Cusp forms 32 24 8
Eisenstein series 16 8 8

Trace form

\( 24q + 4q^{2} - 18q^{3} + 88q^{4} + 120q^{5} - 156q^{6} - 312q^{7} - 228q^{8} + O(q^{10}) \) \( 24q + 4q^{2} - 18q^{3} + 88q^{4} + 120q^{5} - 156q^{6} - 312q^{7} - 228q^{8} + 1800q^{10} + 1168q^{11} - 444q^{12} - 2904q^{13} - 5976q^{14} - 3450q^{15} + 4720q^{16} + 2656q^{17} + 6324q^{18} + 3376q^{19} + 2540q^{20} + 1776q^{21} - 3448q^{22} + 264q^{23} + 3888q^{24} + 6360q^{25} + 1576q^{26} - 14418q^{27} - 11624q^{28} + 5072q^{29} - 20040q^{30} - 40608q^{31} - 27052q^{32} + 288q^{33} + 8296q^{34} + 21560q^{35} + 75864q^{36} + 70728q^{37} + 56104q^{38} + 12852q^{39} - 1880q^{40} - 14800q^{41} - 75696q^{42} - 71880q^{43} - 77320q^{44} - 30960q^{45} - 92088q^{46} - 1160q^{47} + 25140q^{48} + 13264q^{49} + 55900q^{50} + 143820q^{51} + 265296q^{52} + 19744q^{53} + 20412q^{54} + 90800q^{55} - 68160q^{56} - 144576q^{57} - 206952q^{58} - 106496q^{59} - 331320q^{60} - 239184q^{61} - 19704q^{62} + 124248q^{63} + 176840q^{64} + 138160q^{65} + 238848q^{66} + 108456q^{67} + 240728q^{68} + 161784q^{69} + 202920q^{70} - 111184q^{71} - 347148q^{72} - 178536q^{73} - 222496q^{74} - 211170q^{75} - 211408q^{76} + 29856q^{77} + 330744q^{78} + 217840q^{79} + 171500q^{80} + 378504q^{81} + 393896q^{82} + 20952q^{83} + 203616q^{84} - 86760q^{85} - 58832q^{86} - 388092q^{87} - 642168q^{88} - 293664q^{89} - 432600q^{90} - 549168q^{91} - 169632q^{92} - 163008q^{93} - 425768q^{94} + 135760q^{95} + 563568q^{96} + 525576q^{97} + 236084q^{98} + 40176q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)

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
15.6.a \(\chi_{15}(1, \cdot)\) 15.6.a.a 1 1
15.6.a.b 1
15.6.a.c 2
15.6.b \(\chi_{15}(4, \cdot)\) 15.6.b.a 4 1
15.6.e \(\chi_{15}(2, \cdot)\) 15.6.e.a 16 2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(15)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)