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

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

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

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