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Properties

Label 15.3
Level 15
Weight 3
Dimension 8
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 48
Trace bound 3

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(15))\).

Total New Old
Modular forms 24 12 12
Cusp forms 8 8 0
Eisenstein series 16 4 12

Trace form

\( 8 q - 4 q^{2} - 4 q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{7} + 12 q^{8} + 16 q^{9} + O(q^{10}) \) \( 8 q - 4 q^{2} - 4 q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{7} + 12 q^{8} + 16 q^{9} + 24 q^{10} + 16 q^{11} + 28 q^{12} - 16 q^{15} - 48 q^{16} - 40 q^{17} - 52 q^{18} - 48 q^{19} - 36 q^{20} + 40 q^{22} + 56 q^{23} + 72 q^{24} + 56 q^{25} + 88 q^{26} + 44 q^{27} + 56 q^{28} - 44 q^{30} - 48 q^{31} - 76 q^{32} - 56 q^{33} - 8 q^{34} - 40 q^{35} - 40 q^{36} + 32 q^{37} - 96 q^{38} - 64 q^{39} + 8 q^{40} - 56 q^{41} - 48 q^{42} + 24 q^{43} + 76 q^{45} - 8 q^{46} + 128 q^{47} + 124 q^{48} + 72 q^{49} + 164 q^{50} + 136 q^{51} - 112 q^{52} + 56 q^{53} + 16 q^{54} - 144 q^{55} - 64 q^{57} - 152 q^{58} + 16 q^{60} + 128 q^{61} + 88 q^{62} + 24 q^{63} - 56 q^{64} - 112 q^{65} - 16 q^{66} - 152 q^{67} - 104 q^{68} - 264 q^{69} - 120 q^{70} - 272 q^{71} - 156 q^{72} - 72 q^{73} + 44 q^{75} + 448 q^{76} + 88 q^{77} + 280 q^{78} + 472 q^{79} + 164 q^{80} - 32 q^{81} + 408 q^{82} - 16 q^{83} - 24 q^{84} + 72 q^{85} - 224 q^{86} + 56 q^{87} + 72 q^{88} - 16 q^{90} - 208 q^{91} + 104 q^{92} - 248 q^{94} + 144 q^{95} - 352 q^{96} - 352 q^{97} - 188 q^{98} + 80 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)

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
15.3.c \(\chi_{15}(11, \cdot)\) 15.3.c.a 2 1
15.3.d \(\chi_{15}(14, \cdot)\) 15.3.d.a 1 1
15.3.d.b 1
15.3.f \(\chi_{15}(7, \cdot)\) 15.3.f.a 4 2