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Properties

Label 15.5
Level 15
Weight 5
Dimension 20
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 80
Trace bound 3

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(80\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(15))\).

Total New Old
Modular forms 40 24 16
Cusp forms 24 20 4
Eisenstein series 16 4 12

Trace form

\( 20 q + 8 q^{3} - 8 q^{4} - 84 q^{5} - 32 q^{6} + 96 q^{7} + 180 q^{8} + 136 q^{9} + O(q^{10}) \) \( 20 q + 8 q^{3} - 8 q^{4} - 84 q^{5} - 32 q^{6} + 96 q^{7} + 180 q^{8} + 136 q^{9} - 116 q^{10} - 288 q^{11} - 812 q^{12} - 764 q^{13} + 764 q^{15} + 1536 q^{16} + 900 q^{17} + 1160 q^{18} + 512 q^{19} + 564 q^{20} + 384 q^{21} - 760 q^{22} - 1560 q^{23} - 4248 q^{24} - 2884 q^{25} - 3024 q^{26} - 352 q^{27} - 184 q^{28} + 1876 q^{30} - 448 q^{31} + 4980 q^{32} + 7120 q^{33} + 11992 q^{34} + 6600 q^{35} + 1088 q^{36} - 1924 q^{37} - 7680 q^{38} - 8824 q^{39} - 15312 q^{40} - 2712 q^{41} - 9360 q^{42} - 8624 q^{43} + 6976 q^{45} + 15112 q^{46} + 4800 q^{47} + 18268 q^{48} + 12152 q^{49} + 3744 q^{50} - 3824 q^{51} + 7736 q^{52} + 1020 q^{53} - 19664 q^{54} - 14304 q^{55} - 30720 q^{56} - 16984 q^{57} - 21400 q^{58} + 18136 q^{60} + 10944 q^{61} + 28680 q^{62} + 15336 q^{63} + 13704 q^{64} - 1212 q^{65} + 6608 q^{66} + 4896 q^{67} - 1920 q^{68} - 624 q^{69} + 600 q^{70} + 7536 q^{71} - 6900 q^{72} + 12196 q^{73} + 2384 q^{75} + 2592 q^{76} - 360 q^{77} - 6080 q^{78} - 21848 q^{79} + 10644 q^{80} - 3500 q^{81} - 58440 q^{82} - 32400 q^{83} - 17544 q^{84} - 30788 q^{85} + 14592 q^{86} + 5720 q^{87} + 1320 q^{88} - 14716 q^{90} + 19872 q^{91} - 31800 q^{92} + 5856 q^{93} + 63112 q^{94} + 18864 q^{95} + 19808 q^{96} + 68396 q^{97} + 46440 q^{98} + 37760 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(15))\)

We only show spaces with odd 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
15.5.c \(\chi_{15}(11, \cdot)\) 15.5.c.a 6 1
15.5.d \(\chi_{15}(14, \cdot)\) 15.5.d.a 1 1
15.5.d.b 1
15.5.d.c 4
15.5.f \(\chi_{15}(7, \cdot)\) 15.5.f.a 8 2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces

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