# Properties

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

## 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

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

## 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

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