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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

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

Display 100 coefficients 10 coefficients

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 available 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

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