Properties

Label 24.3
Level 24
Weight 3
Dimension 12
Nonzero newspaces 3
Newforms 5
Sturm bound 96
Trace bound 1

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 5 \)
Sturm bound: \(96\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(24))\).

Total New Old
Modular forms 44 16 28
Cusp forms 20 12 8
Eisenstein series 24 4 20

Trace form

\(12q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{4} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 16q^{7} \) \(\mathstrut -\mathstrut 4q^{8} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{4} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 16q^{7} \) \(\mathstrut -\mathstrut 4q^{8} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 16q^{12} \) \(\mathstrut +\mathstrut 20q^{13} \) \(\mathstrut +\mathstrut 36q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 32q^{16} \) \(\mathstrut -\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 62q^{18} \) \(\mathstrut +\mathstrut 36q^{19} \) \(\mathstrut +\mathstrut 72q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 48q^{22} \) \(\mathstrut -\mathstrut 52q^{24} \) \(\mathstrut -\mathstrut 72q^{25} \) \(\mathstrut -\mathstrut 96q^{26} \) \(\mathstrut -\mathstrut 46q^{27} \) \(\mathstrut -\mathstrut 176q^{28} \) \(\mathstrut -\mathstrut 172q^{30} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 88q^{32} \) \(\mathstrut +\mathstrut 20q^{33} \) \(\mathstrut -\mathstrut 68q^{34} \) \(\mathstrut +\mathstrut 96q^{35} \) \(\mathstrut +\mathstrut 108q^{36} \) \(\mathstrut -\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 40q^{38} \) \(\mathstrut +\mathstrut 132q^{39} \) \(\mathstrut +\mathstrut 248q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 220q^{42} \) \(\mathstrut +\mathstrut 196q^{43} \) \(\mathstrut +\mathstrut 64q^{44} \) \(\mathstrut +\mathstrut 64q^{45} \) \(\mathstrut +\mathstrut 152q^{46} \) \(\mathstrut -\mathstrut 72q^{48} \) \(\mathstrut -\mathstrut 100q^{49} \) \(\mathstrut -\mathstrut 118q^{50} \) \(\mathstrut -\mathstrut 224q^{51} \) \(\mathstrut -\mathstrut 160q^{52} \) \(\mathstrut -\mathstrut 202q^{54} \) \(\mathstrut -\mathstrut 296q^{55} \) \(\mathstrut -\mathstrut 168q^{56} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 4q^{58} \) \(\mathstrut -\mathstrut 128q^{59} \) \(\mathstrut +\mathstrut 48q^{60} \) \(\mathstrut -\mathstrut 172q^{61} \) \(\mathstrut +\mathstrut 204q^{62} \) \(\mathstrut -\mathstrut 176q^{63} \) \(\mathstrut +\mathstrut 240q^{64} \) \(\mathstrut +\mathstrut 96q^{65} \) \(\mathstrut +\mathstrut 216q^{66} \) \(\mathstrut -\mathstrut 252q^{67} \) \(\mathstrut +\mathstrut 112q^{68} \) \(\mathstrut -\mathstrut 64q^{69} \) \(\mathstrut +\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 124q^{72} \) \(\mathstrut +\mathstrut 440q^{73} \) \(\mathstrut -\mathstrut 120q^{74} \) \(\mathstrut +\mathstrut 178q^{75} \) \(\mathstrut -\mathstrut 72q^{76} \) \(\mathstrut -\mathstrut 160q^{78} \) \(\mathstrut +\mathstrut 400q^{79} \) \(\mathstrut -\mathstrut 96q^{80} \) \(\mathstrut +\mathstrut 108q^{81} \) \(\mathstrut -\mathstrut 348q^{82} \) \(\mathstrut +\mathstrut 160q^{83} \) \(\mathstrut +\mathstrut 88q^{84} \) \(\mathstrut +\mathstrut 256q^{85} \) \(\mathstrut +\mathstrut 88q^{86} \) \(\mathstrut +\mathstrut 492q^{87} \) \(\mathstrut -\mathstrut 48q^{88} \) \(\mathstrut -\mathstrut 200q^{89} \) \(\mathstrut +\mathstrut 44q^{90} \) \(\mathstrut +\mathstrut 168q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut -\mathstrut 44q^{93} \) \(\mathstrut -\mathstrut 168q^{94} \) \(\mathstrut -\mathstrut 40q^{96} \) \(\mathstrut -\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut 170q^{98} \) \(\mathstrut -\mathstrut 32q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)

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
24.3.b \(\chi_{24}(19, \cdot)\) 24.3.b.a 4 1
24.3.e \(\chi_{24}(17, \cdot)\) 24.3.e.a 2 1
24.3.g \(\chi_{24}(7, \cdot)\) None 0 1
24.3.h \(\chi_{24}(5, \cdot)\) 24.3.h.a 1 1
24.3.h.b 1
24.3.h.c 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(24))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(24)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)