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Properties

Label 960.2
Level 960
Weight 2
Dimension 9372
Nonzero newspaces 28
Newform subspaces 128
Sturm bound 98304
Trace bound 22

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Defining parameters

Level: \( N \) = \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 28 \)
Newform subspaces: \( 128 \)
Sturm bound: \(98304\)
Trace bound: \(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(960))\).

Total New Old
Modular forms 25728 9636 16092
Cusp forms 23425 9372 14053
Eisenstein series 2303 264 2039

Trace form

\( 9372 q - 12 q^{3} - 32 q^{4} - 48 q^{6} - 32 q^{7} - 20 q^{9} + O(q^{10}) \) \( 9372 q - 12 q^{3} - 32 q^{4} - 48 q^{6} - 32 q^{7} - 20 q^{9} - 48 q^{10} - 16 q^{11} - 16 q^{12} - 64 q^{13} - 24 q^{15} - 96 q^{16} - 32 q^{17} - 16 q^{18} - 56 q^{19} - 40 q^{21} + 64 q^{24} - 28 q^{25} + 160 q^{26} + 12 q^{27} + 128 q^{28} + 64 q^{29} + 56 q^{30} + 16 q^{31} + 160 q^{32} + 64 q^{33} + 128 q^{34} + 24 q^{35} + 112 q^{36} + 32 q^{37} + 160 q^{38} + 40 q^{39} + 32 q^{40} + 64 q^{41} + 64 q^{42} - 8 q^{43} + 32 q^{44} + 20 q^{45} - 96 q^{46} - 16 q^{48} - 28 q^{49} - 48 q^{50} + 96 q^{51} - 224 q^{52} - 48 q^{54} + 120 q^{55} - 224 q^{56} + 56 q^{57} - 320 q^{58} + 320 q^{59} - 120 q^{60} - 96 q^{61} - 192 q^{62} + 112 q^{63} - 416 q^{64} + 80 q^{65} - 208 q^{66} + 424 q^{67} - 192 q^{68} + 8 q^{69} - 240 q^{70} + 384 q^{71} - 16 q^{72} + 88 q^{73} - 224 q^{74} + 152 q^{75} - 352 q^{76} + 96 q^{77} - 160 q^{78} + 208 q^{79} - 48 q^{80} - 84 q^{81} - 32 q^{82} + 80 q^{83} - 240 q^{84} + 96 q^{85} - 16 q^{87} - 32 q^{88} + 64 q^{89} - 168 q^{90} - 64 q^{91} - 32 q^{93} - 32 q^{94} + 48 q^{95} - 320 q^{96} - 56 q^{97} - 56 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(960))\)

We only show spaces with even 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
960.2.a \(\chi_{960}(1, \cdot)\) 960.2.a.a 1 1
960.2.a.b 1
960.2.a.c 1
960.2.a.d 1
960.2.a.e 1
960.2.a.f 1
960.2.a.g 1
960.2.a.h 1
960.2.a.i 1
960.2.a.j 1
960.2.a.k 1
960.2.a.l 1
960.2.a.m 1
960.2.a.n 1
960.2.a.o 1
960.2.a.p 1
960.2.b \(\chi_{960}(671, \cdot)\) 960.2.b.a 4 1
960.2.b.b 4
960.2.b.c 12
960.2.b.d 12
960.2.d \(\chi_{960}(289, \cdot)\) 960.2.d.a 2 1
960.2.d.b 2
960.2.d.c 2
960.2.d.d 2
960.2.d.e 8
960.2.d.f 8
960.2.f \(\chi_{960}(769, \cdot)\) 960.2.f.a 2 1
960.2.f.b 2
960.2.f.c 2
960.2.f.d 2
960.2.f.e 2
960.2.f.f 2
960.2.f.g 2
960.2.f.h 2
960.2.f.i 2
960.2.f.j 2
960.2.f.k 4
960.2.h \(\chi_{960}(191, \cdot)\) 960.2.h.a 4 1
960.2.h.b 4
960.2.h.c 4
960.2.h.d 4
960.2.h.e 4
960.2.h.f 4
960.2.h.g 8
960.2.k \(\chi_{960}(481, \cdot)\) 960.2.k.a 2 1
960.2.k.b 2
960.2.k.c 2
960.2.k.d 2
960.2.k.e 4
960.2.k.f 4
960.2.m \(\chi_{960}(479, \cdot)\) 960.2.m.a 8 1
960.2.m.b 8
960.2.m.c 16
960.2.m.d 16
960.2.o \(\chi_{960}(959, \cdot)\) 960.2.o.a 4 1
960.2.o.b 4
960.2.o.c 4
960.2.o.d 8
960.2.o.e 24
960.2.s \(\chi_{960}(241, \cdot)\) 960.2.s.a 4 2
960.2.s.b 8
960.2.s.c 20
960.2.t \(\chi_{960}(239, \cdot)\) 960.2.t.a 8 2
960.2.t.b 80
960.2.v \(\chi_{960}(257, \cdot)\) 960.2.v.a 4 2
960.2.v.b 4
960.2.v.c 4
960.2.v.d 4
960.2.v.e 4
960.2.v.f 4
960.2.v.g 4
960.2.v.h 4
960.2.v.i 4
960.2.v.j 4
960.2.v.k 4
960.2.v.l 4
960.2.v.m 16
960.2.v.n 24
960.2.w \(\chi_{960}(127, \cdot)\) 960.2.w.a 4 2
960.2.w.b 4
960.2.w.c 4
960.2.w.d 8
960.2.w.e 8
960.2.w.f 8
960.2.w.g 12
960.2.y \(\chi_{960}(847, \cdot)\) 960.2.y.a 2 2
960.2.y.b 2
960.2.y.c 2
960.2.y.d 6
960.2.y.e 16
960.2.y.f 20
960.2.bb \(\chi_{960}(497, \cdot)\) 960.2.bb.a 88 2
960.2.bc \(\chi_{960}(367, \cdot)\) 960.2.bc.a 2 2
960.2.bc.b 2
960.2.bc.c 2
960.2.bc.d 6
960.2.bc.e 16
960.2.bc.f 20
960.2.bf \(\chi_{960}(17, \cdot)\) 960.2.bf.a 88 2
960.2.bh \(\chi_{960}(223, \cdot)\) 960.2.bh.a 4 2
960.2.bh.b 4
960.2.bh.c 4
960.2.bh.d 4
960.2.bh.e 8
960.2.bh.f 8
960.2.bh.g 8
960.2.bh.h 8
960.2.bi \(\chi_{960}(353, \cdot)\) 960.2.bi.a 4 2
960.2.bi.b 4
960.2.bi.c 4
960.2.bi.d 4
960.2.bi.e 8
960.2.bi.f 8
960.2.bi.g 32
960.2.bi.h 32
960.2.bk \(\chi_{960}(431, \cdot)\) 960.2.bk.a 4 2
960.2.bk.b 60
960.2.bl \(\chi_{960}(49, \cdot)\) 960.2.bl.a 48 2
960.2.bo \(\chi_{960}(103, \cdot)\) None 0 4
960.2.br \(\chi_{960}(233, \cdot)\) None 0 4
960.2.bs \(\chi_{960}(119, \cdot)\) None 0 4
960.2.bv \(\chi_{960}(121, \cdot)\) None 0 4
960.2.bx \(\chi_{960}(71, \cdot)\) None 0 4
960.2.by \(\chi_{960}(169, \cdot)\) None 0 4
960.2.cb \(\chi_{960}(137, \cdot)\) None 0 4
960.2.cc \(\chi_{960}(7, \cdot)\) None 0 4
960.2.cf \(\chi_{960}(173, \cdot)\) 960.2.cf.a 1504 8
960.2.cg \(\chi_{960}(43, \cdot)\) 960.2.cg.a 768 8
960.2.ci \(\chi_{960}(61, \cdot)\) 960.2.ci.a 240 8
960.2.ci.b 272
960.2.ck \(\chi_{960}(109, \cdot)\) 960.2.ck.a 768 8
960.2.cn \(\chi_{960}(11, \cdot)\) 960.2.cn.a 1024 8
960.2.cp \(\chi_{960}(59, \cdot)\) 960.2.cp.a 32 8
960.2.cp.b 1472
960.2.cr \(\chi_{960}(53, \cdot)\) 960.2.cr.a 1504 8
960.2.cs \(\chi_{960}(163, \cdot)\) 960.2.cs.a 768 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(960))\) into lower level spaces

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