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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

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

Display 100 coefficients 10 coefficients

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 available 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

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