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Properties

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

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
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

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

Display 100 coefficients 10 coefficients

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 available 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

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