Properties

Label 48.3
Level 48
Weight 3
Dimension 49
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 384
Trace bound 1

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Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(384\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(48))\).

Total New Old
Modular forms 156 59 97
Cusp forms 100 49 51
Eisenstein series 56 10 46

Trace form

\( 49q - q^{3} + 8q^{4} + 12q^{5} + 4q^{6} + 10q^{7} - 12q^{8} - 11q^{9} + O(q^{10}) \) \( 49q - q^{3} + 8q^{4} + 12q^{5} + 4q^{6} + 10q^{7} - 12q^{8} - 11q^{9} - 80q^{10} + 32q^{11} - 56q^{12} - 34q^{13} - 44q^{14} - 36q^{15} + 16q^{16} - 12q^{17} - 48q^{18} - 98q^{19} + 80q^{20} - 26q^{21} + 72q^{22} - 128q^{23} - 20q^{24} + 33q^{25} - 100q^{26} + 23q^{27} + 92q^{29} + 156q^{30} + 82q^{31} + 160q^{32} + 100q^{33} + 232q^{34} + 96q^{35} + 208q^{36} - 34q^{37} + 168q^{38} - 86q^{39} + 136q^{40} - 108q^{41} + 220q^{42} - 50q^{43} + 88q^{44} - 24q^{45} - 64q^{46} - 32q^{48} + 7q^{49} - 236q^{50} + 128q^{51} - 368q^{52} - 196q^{53} - 164q^{54} - 192q^{55} - 224q^{56} - 50q^{57} - 424q^{58} - 128q^{59} - 648q^{60} - 306q^{61} - 276q^{62} + 90q^{63} - 640q^{64} - 200q^{65} - 500q^{66} + 318q^{67} - 448q^{68} + 12q^{69} - 72q^{70} + 512q^{71} - 252q^{72} + 282q^{73} + 348q^{74} + 459q^{75} + 848q^{76} + 512q^{77} + 632q^{78} + 370q^{79} + 552q^{80} - 15q^{81} + 696q^{82} - 160q^{83} + 952q^{84} + 280q^{85} + 528q^{86} - 96q^{87} + 832q^{88} + 228q^{89} + 984q^{90} - 28q^{91} + 496q^{92} - 46q^{93} - 24q^{94} + 8q^{96} - 126q^{97} - 440q^{98} - 260q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.3.b \(\chi_{48}(7, \cdot)\) None 0 1
48.3.e \(\chi_{48}(17, \cdot)\) 48.3.e.a 1 1
48.3.e.b 2
48.3.g \(\chi_{48}(31, \cdot)\) 48.3.g.a 2 1
48.3.h \(\chi_{48}(41, \cdot)\) None 0 1
48.3.i \(\chi_{48}(5, \cdot)\) 48.3.i.a 8 2
48.3.i.b 20
48.3.l \(\chi_{48}(19, \cdot)\) 48.3.l.a 16 2

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(48)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)