Properties

Label 960.3
Level 960
Weight 3
Dimension 18876
Nonzero newspaces 28
Sturm bound 147456
Trace bound 22

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Defining parameters

Level: \( N \) = \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 28 \)
Sturm bound: \(147456\)
Trace bound: \(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(960))\).

Total New Old
Modular forms 50304 19140 31164
Cusp forms 48000 18876 29124
Eisenstein series 2304 264 2040

Trace form

\( 18876q - 12q^{3} - 32q^{4} - 48q^{6} - 16q^{7} - 20q^{9} + O(q^{10}) \) \( 18876q - 12q^{3} - 32q^{4} - 48q^{6} - 16q^{7} - 20q^{9} - 48q^{10} + 64q^{11} - 16q^{12} + 32q^{13} - 20q^{15} - 96q^{16} - 64q^{17} - 16q^{18} - 152q^{19} - 216q^{21} - 320q^{22} - 256q^{23} - 576q^{24} - 252q^{25} - 800q^{26} - 108q^{27} - 512q^{28} - 128q^{29} - 104q^{30} - 112q^{31} + 160q^{32} + 80q^{33} + 448q^{34} + 96q^{35} + 752q^{36} + 352q^{37} + 1120q^{38} - 16q^{39} + 672q^{40} + 640q^{41} + 864q^{42} + 168q^{43} + 416q^{44} + 28q^{45} - 96q^{46} - 16q^{48} - 252q^{49} + 624q^{50} - 800q^{51} + 2080q^{52} + 272q^{54} - 1312q^{55} + 1568q^{56} + 72q^{57} + 1408q^{58} - 1280q^{59} + 264q^{60} - 96q^{61} + 192q^{62} - 416q^{64} - 608q^{65} - 560q^{66} + 1000q^{67} - 960q^{68} - 424q^{69} - 1392q^{70} + 2048q^{71} - 16q^{72} + 216q^{73} - 2464q^{74} + 624q^{75} - 3424q^{76} - 192q^{77} - 640q^{78} + 2544q^{79} - 816q^{80} + 940q^{81} - 32q^{82} + 320q^{83} + 2448q^{84} + 816q^{85} + 888q^{87} - 32q^{88} + 640q^{89} + 696q^{90} + 1088q^{91} + 992q^{93} - 32q^{94} + 1536q^{95} - 320q^{96} + 1448q^{97} + 248q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(960))\)

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
960.3.c \(\chi_{960}(449, \cdot)\) 960.3.c.a 1 1
960.3.c.b 1
960.3.c.c 1
960.3.c.d 1
960.3.c.e 4
960.3.c.f 4
960.3.c.g 4
960.3.c.h 4
960.3.c.i 8
960.3.c.j 12
960.3.c.k 12
960.3.c.l 16
960.3.c.m 24
960.3.e \(\chi_{960}(511, \cdot)\) 960.3.e.a 4 1
960.3.e.b 4
960.3.e.c 8
960.3.e.d 8
960.3.e.e 8
960.3.g \(\chi_{960}(31, \cdot)\) 960.3.g.a 8 1
960.3.g.b 8
960.3.g.c 16
960.3.i \(\chi_{960}(929, \cdot)\) 960.3.i.a 32 1
960.3.i.b 64
960.3.j \(\chi_{960}(319, \cdot)\) 960.3.j.a 4 1
960.3.j.b 4
960.3.j.c 4
960.3.j.d 4
960.3.j.e 8
960.3.j.f 12
960.3.j.g 12
960.3.l \(\chi_{960}(641, \cdot)\) 960.3.l.a 2 1
960.3.l.b 2
960.3.l.c 2
960.3.l.d 2
960.3.l.e 4
960.3.l.f 4
960.3.l.g 8
960.3.l.h 8
960.3.l.i 16
960.3.l.j 16
960.3.n \(\chi_{960}(161, \cdot)\) 960.3.n.a 24 1
960.3.n.b 40
960.3.p \(\chi_{960}(799, \cdot)\) 960.3.p.a 8 1
960.3.p.b 8
960.3.p.c 16
960.3.p.d 16
960.3.q \(\chi_{960}(79, \cdot)\) 960.3.q.a 96 2
960.3.r \(\chi_{960}(401, \cdot)\) n/a 128 2
960.3.u \(\chi_{960}(287, \cdot)\) n/a 192 2
960.3.x \(\chi_{960}(97, \cdot)\) 960.3.x.a 8 2
960.3.x.b 8
960.3.x.c 16
960.3.x.d 16
960.3.x.e 24
960.3.x.f 24
960.3.z \(\chi_{960}(527, \cdot)\) n/a 184 2
960.3.ba \(\chi_{960}(817, \cdot)\) 960.3.ba.a 96 2
960.3.bd \(\chi_{960}(47, \cdot)\) n/a 184 2
960.3.be \(\chi_{960}(337, \cdot)\) 960.3.be.a 96 2
960.3.bg \(\chi_{960}(193, \cdot)\) 960.3.bg.a 4 2
960.3.bg.b 4
960.3.bg.c 4
960.3.bg.d 4
960.3.bg.e 4
960.3.bg.f 4
960.3.bg.g 4
960.3.bg.h 4
960.3.bg.i 4
960.3.bg.j 8
960.3.bg.k 8
960.3.bg.l 8
960.3.bg.m 12
960.3.bg.n 12
960.3.bg.o 12
960.3.bj \(\chi_{960}(383, \cdot)\) n/a 184 2
960.3.bm \(\chi_{960}(209, \cdot)\) n/a 184 2
960.3.bn \(\chi_{960}(271, \cdot)\) 960.3.bn.a 64 2
960.3.bp \(\chi_{960}(73, \cdot)\) None 0 4
960.3.bq \(\chi_{960}(263, \cdot)\) None 0 4
960.3.bt \(\chi_{960}(151, \cdot)\) None 0 4
960.3.bu \(\chi_{960}(89, \cdot)\) None 0 4
960.3.bw \(\chi_{960}(199, \cdot)\) None 0 4
960.3.bz \(\chi_{960}(41, \cdot)\) None 0 4
960.3.ca \(\chi_{960}(23, \cdot)\) None 0 4
960.3.cd \(\chi_{960}(313, \cdot)\) None 0 4
960.3.ce \(\chi_{960}(133, \cdot)\) n/a 1536 8
960.3.ch \(\chi_{960}(83, \cdot)\) n/a 3040 8
960.3.cj \(\chi_{960}(101, \cdot)\) n/a 2048 8
960.3.cl \(\chi_{960}(29, \cdot)\) n/a 3040 8
960.3.cm \(\chi_{960}(91, \cdot)\) n/a 1024 8
960.3.co \(\chi_{960}(19, \cdot)\) n/a 1536 8
960.3.cq \(\chi_{960}(13, \cdot)\) n/a 1536 8
960.3.ct \(\chi_{960}(203, \cdot)\) n/a 3040 8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(960))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(960)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 2}\)