Properties

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

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 4 \)
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

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

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 the 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