Properties

Label 288.3
Level 288
Weight 3
Dimension 2007
Nonzero newspaces 12
Newform subspaces 27
Sturm bound 13824
Trace bound 13

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Defining parameters

Level: \( N \) = \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 27 \)
Sturm bound: \(13824\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(288))\).

Total New Old
Modular forms 4864 2097 2767
Cusp forms 4352 2007 2345
Eisenstein series 512 90 422

Trace form

\( 2007q - 12q^{2} - 12q^{3} - 12q^{4} - 8q^{5} - 16q^{6} - 10q^{7} - 12q^{8} - 24q^{9} + O(q^{10}) \) \( 2007q - 12q^{2} - 12q^{3} - 12q^{4} - 8q^{5} - 16q^{6} - 10q^{7} - 12q^{8} - 24q^{9} - 76q^{10} - 28q^{11} - 16q^{12} - 40q^{13} - 28q^{14} - 30q^{15} + 8q^{16} - 62q^{17} - 16q^{18} - 58q^{19} + 68q^{20} - 48q^{21} + 136q^{22} - 70q^{23} - 16q^{24} + 31q^{25} + 88q^{26} + 36q^{27} + 24q^{28} + 152q^{29} + 16q^{30} + 122q^{31} - 32q^{32} + 76q^{33} - 56q^{34} + 288q^{35} + 248q^{36} + 224q^{37} + 604q^{38} + 102q^{39} + 480q^{40} + 294q^{41} + 384q^{42} + 200q^{43} + 332q^{44} + 80q^{45} + 60q^{46} + 6q^{47} - 120q^{48} - 113q^{49} - 324q^{50} - 56q^{51} - 228q^{52} - 616q^{53} - 632q^{54} - 128q^{55} - 896q^{56} - 120q^{57} - 888q^{58} + 52q^{59} - 744q^{60} - 520q^{61} - 576q^{62} + 210q^{63} - 264q^{64} - 92q^{65} - 16q^{66} - 296q^{67} - 632q^{68} + 112q^{69} - 672q^{70} - 268q^{71} - 16q^{72} + 34q^{73} - 540q^{74} - 4q^{75} - 524q^{76} - 44q^{77} - 424q^{78} + 882q^{79} - 1616q^{80} - 424q^{81} - 1476q^{82} + 1508q^{83} - 1248q^{84} + 384q^{85} - 1192q^{86} + 706q^{87} - 456q^{88} + 310q^{89} - 736q^{90} + 936q^{91} - 304q^{92} - 16q^{93} - 96q^{94} - 168q^{95} + 120q^{96} - 278q^{97} + 416q^{98} - 814q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(288))\)

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
288.3.b \(\chi_{288}(271, \cdot)\) 288.3.b.a 1 1
288.3.b.b 4
288.3.b.c 4
288.3.e \(\chi_{288}(161, \cdot)\) 288.3.e.a 2 1
288.3.e.b 2
288.3.e.c 2
288.3.e.d 2
288.3.g \(\chi_{288}(127, \cdot)\) 288.3.g.a 2 1
288.3.g.b 2
288.3.g.c 2
288.3.g.d 4
288.3.h \(\chi_{288}(17, \cdot)\) 288.3.h.a 8 1
288.3.j \(\chi_{288}(89, \cdot)\) None 0 2
288.3.m \(\chi_{288}(55, \cdot)\) None 0 2
288.3.n \(\chi_{288}(113, \cdot)\) 288.3.n.a 44 2
288.3.o \(\chi_{288}(31, \cdot)\) 288.3.o.a 4 2
288.3.o.b 20
288.3.o.c 24
288.3.q \(\chi_{288}(65, \cdot)\) 288.3.q.a 24 2
288.3.q.b 24
288.3.t \(\chi_{288}(79, \cdot)\) 288.3.t.a 4 2
288.3.t.b 40
288.3.u \(\chi_{288}(19, \cdot)\) 288.3.u.a 28 4
288.3.u.b 64
288.3.u.c 64
288.3.x \(\chi_{288}(53, \cdot)\) 288.3.x.a 64 4
288.3.x.b 64
288.3.z \(\chi_{288}(7, \cdot)\) None 0 4
288.3.ba \(\chi_{288}(41, \cdot)\) None 0 4
288.3.bd \(\chi_{288}(43, \cdot)\) 288.3.bd.a 752 8
288.3.be \(\chi_{288}(5, \cdot)\) 288.3.be.a 752 8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(288))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(288)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)