Properties

Label 15.12
Level 15
Weight 12
Dimension 60
Nonzero newspaces 3
Newforms 6
Sturm bound 192
Trace bound 1

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 6 \)
Sturm bound: \(192\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(15))\).

Total New Old
Modular forms 96 68 28
Cusp forms 80 60 20
Eisenstein series 16 8 8

Trace form

\( 60q - 92q^{2} + 990q^{3} - 14216q^{4} + 2556q^{5} + 18492q^{6} + 41800q^{7} + 36156q^{8} - 236196q^{9} + O(q^{10}) \) \( 60q - 92q^{2} + 990q^{3} - 14216q^{4} + 2556q^{5} + 18492q^{6} + 41800q^{7} + 36156q^{8} - 236196q^{9} + 457304q^{10} + 40816q^{11} - 221196q^{12} - 5180664q^{13} + 7691784q^{14} - 2824266q^{15} - 17008528q^{16} + 15690832q^{17} - 1703388q^{18} - 22515568q^{19} - 18644116q^{20} + 49972368q^{21} + 59074504q^{22} - 54036408q^{23} - 20190384q^{24} - 190902324q^{25} + 270157000q^{26} + 141980526q^{27} + 46370936q^{28} - 803020696q^{29} + 332463216q^{30} + 661335632q^{31} + 392770196q^{32} - 564588576q^{33} - 1584653272q^{34} + 55480040q^{35} + 2203314168q^{36} + 1703958440q^{37} + 925664872q^{38} - 1071207180q^{39} - 3241136952q^{40} - 3710760328q^{41} - 5172070272q^{42} + 7394860968q^{43} + 7318559096q^{44} + 4843518156q^{45} - 8257792888q^{46} - 6579674120q^{47} - 13360704396q^{48} + 6452219836q^{49} + 16211013724q^{50} + 8974556460q^{51} - 1169845744q^{52} + 2398000672q^{53} + 401769396q^{54} - 21206572944q^{55} - 36336264000q^{56} - 10998223488q^{57} + 40589376184q^{58} + 13057177408q^{59} + 49070647896q^{60} - 8363902856q^{61} - 14092986648q^{62} - 49763144328q^{63} - 32394859192q^{64} + 24411443968q^{65} + 108654800640q^{66} + 54710233816q^{67} - 16371169096q^{68} - 46243753416q^{69} - 137630773080q^{70} + 334955600q^{71} - 90848138796q^{72} + 64595867160q^{73} + 15096746144q^{74} + 87585859374q^{75} + 110178455344q^{76} + 39494634432q^{77} - 110669222328q^{78} - 112559264640q^{79} - 42984538996q^{80} + 46799565660q^{81} - 64018291128q^{82} + 29154140856q^{83} - 53057428704q^{84} + 56305104632q^{85} + 193108576336q^{86} + 101261120676q^{87} - 10684977144q^{88} - 203915821368q^{89} + 143487624q^{90} + 12362579792q^{91} - 185727975744q^{92} + 142951443264q^{93} + 483713682200q^{94} + 196144152304q^{95} - 657593597712q^{96} - 680585742184q^{97} - 216115979308q^{98} + 40384792080q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(15))\)

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
15.12.a \(\chi_{15}(1, \cdot)\) 15.12.a.a 1 1
15.12.a.b 2
15.12.a.c 2
15.12.a.d 3
15.12.b \(\chi_{15}(4, \cdot)\) 15.12.b.a 12 1
15.12.e \(\chi_{15}(2, \cdot)\) 15.12.e.a 40 2

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(15)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)