# Properties

 Label 1008.2 Level 1008 Weight 2 Dimension 11597 Nonzero newspaces 40 Sturm bound 110592 Trace bound 29

## Defining parameters

 Level: $$N$$ = $$1008 = 2^{4} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$110592$$ Trace bound: $$29$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1008))$$.

Total New Old
Modular forms 28992 12001 16991
Cusp forms 26305 11597 14708
Eisenstein series 2687 404 2283

## Trace form

 $$11597 q - 24 q^{2} - 24 q^{3} - 28 q^{4} - 35 q^{5} - 32 q^{6} - 28 q^{7} - 72 q^{8} - 16 q^{9} + O(q^{10})$$ $$11597 q - 24 q^{2} - 24 q^{3} - 28 q^{4} - 35 q^{5} - 32 q^{6} - 28 q^{7} - 72 q^{8} - 16 q^{9} - 76 q^{10} - 45 q^{11} - 32 q^{12} - 50 q^{13} - 12 q^{14} - 66 q^{15} + 20 q^{16} - 37 q^{17} + 8 q^{18} - 67 q^{19} + 76 q^{20} - 37 q^{21} + 32 q^{22} + 5 q^{23} + 32 q^{24} + 23 q^{25} + 92 q^{26} + 12 q^{27} - 52 q^{28} - 28 q^{29} + 8 q^{30} - 17 q^{31} + 36 q^{32} - 30 q^{33} - 4 q^{34} + 33 q^{35} - 72 q^{36} - 119 q^{37} - 116 q^{38} + 90 q^{39} - 140 q^{40} + 30 q^{41} - 80 q^{42} + 78 q^{43} - 148 q^{44} + 6 q^{45} - 136 q^{46} + 141 q^{47} - 136 q^{48} - 60 q^{49} - 144 q^{50} + 40 q^{51} - 40 q^{52} + 35 q^{53} - 120 q^{54} + 114 q^{55} - 48 q^{56} - 64 q^{57} - 16 q^{58} + 55 q^{59} - 248 q^{60} + 65 q^{61} - 120 q^{62} - 33 q^{63} + 44 q^{64} - 150 q^{65} - 272 q^{66} - 5 q^{67} - 136 q^{68} - 142 q^{69} + 56 q^{70} - 68 q^{71} - 256 q^{72} + 85 q^{73} - 140 q^{74} - 20 q^{75} + 44 q^{76} + 62 q^{77} - 296 q^{78} + 17 q^{79} - 292 q^{80} - 128 q^{81} - 92 q^{82} - 72 q^{83} - 184 q^{84} + 130 q^{85} - 316 q^{86} - 54 q^{87} - 172 q^{88} + 99 q^{89} - 320 q^{90} + 80 q^{91} - 268 q^{92} + 138 q^{93} - 292 q^{94} + 25 q^{95} - 168 q^{96} + 38 q^{97} - 248 q^{98} - 18 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1008))$$

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
1008.2.a $$\chi_{1008}(1, \cdot)$$ 1008.2.a.a 1 1
1008.2.a.b 1
1008.2.a.c 1
1008.2.a.d 1
1008.2.a.e 1
1008.2.a.f 1
1008.2.a.g 1
1008.2.a.h 1
1008.2.a.i 1
1008.2.a.j 1
1008.2.a.k 1
1008.2.a.l 1
1008.2.a.m 1
1008.2.a.n 2
1008.2.b $$\chi_{1008}(559, \cdot)$$ 1008.2.b.a 2 1
1008.2.b.b 2
1008.2.b.c 2
1008.2.b.d 2
1008.2.b.e 2
1008.2.b.f 2
1008.2.b.g 2
1008.2.b.h 2
1008.2.b.i 4
1008.2.c $$\chi_{1008}(505, \cdot)$$ None 0 1
1008.2.h $$\chi_{1008}(575, \cdot)$$ 1008.2.h.a 4 1
1008.2.h.b 8
1008.2.i $$\chi_{1008}(377, \cdot)$$ None 0 1
1008.2.j $$\chi_{1008}(71, \cdot)$$ None 0 1
1008.2.k $$\chi_{1008}(881, \cdot)$$ 1008.2.k.a 4 1
1008.2.k.b 4
1008.2.k.c 8
1008.2.p $$\chi_{1008}(55, \cdot)$$ None 0 1
1008.2.q $$\chi_{1008}(529, \cdot)$$ 1008.2.q.a 2 2
1008.2.q.b 2
1008.2.q.c 2
1008.2.q.d 2
1008.2.q.e 2
1008.2.q.f 2
1008.2.q.g 6
1008.2.q.h 6
1008.2.q.i 10
1008.2.q.j 14
1008.2.q.k 22
1008.2.q.l 22
1008.2.r $$\chi_{1008}(337, \cdot)$$ 1008.2.r.a 2 2
1008.2.r.b 2
1008.2.r.c 2
1008.2.r.d 2
1008.2.r.e 4
1008.2.r.f 4
1008.2.r.g 6
1008.2.r.h 6
1008.2.r.i 6
1008.2.r.j 6
1008.2.r.k 6
1008.2.r.l 8
1008.2.r.m 8
1008.2.r.n 10
1008.2.s $$\chi_{1008}(289, \cdot)$$ 1008.2.s.a 2 2
1008.2.s.b 2
1008.2.s.c 2
1008.2.s.d 2
1008.2.s.e 2
1008.2.s.f 2
1008.2.s.g 2
1008.2.s.h 2
1008.2.s.i 2
1008.2.s.j 2
1008.2.s.k 2
1008.2.s.l 2
1008.2.s.m 2
1008.2.s.n 2
1008.2.s.o 2
1008.2.s.p 2
1008.2.s.q 2
1008.2.s.r 4
1008.2.t $$\chi_{1008}(193, \cdot)$$ 1008.2.t.a 2 2
1008.2.t.b 2
1008.2.t.c 2
1008.2.t.d 2
1008.2.t.e 2
1008.2.t.f 2
1008.2.t.g 6
1008.2.t.h 6
1008.2.t.i 10
1008.2.t.j 14
1008.2.t.k 22
1008.2.t.l 22
1008.2.v $$\chi_{1008}(323, \cdot)$$ 1008.2.v.a 4 2
1008.2.v.b 4
1008.2.v.c 12
1008.2.v.d 36
1008.2.v.e 40
1008.2.x $$\chi_{1008}(307, \cdot)$$ n/a 156 2
1008.2.z $$\chi_{1008}(253, \cdot)$$ n/a 120 2
1008.2.bb $$\chi_{1008}(125, \cdot)$$ n/a 128 2
1008.2.be $$\chi_{1008}(457, \cdot)$$ None 0 2
1008.2.bf $$\chi_{1008}(31, \cdot)$$ 1008.2.bf.a 2 2
1008.2.bf.b 2
1008.2.bf.c 2
1008.2.bf.d 2
1008.2.bf.e 4
1008.2.bf.f 4
1008.2.bf.g 24
1008.2.bf.h 24
1008.2.bf.i 32
1008.2.bg $$\chi_{1008}(185, \cdot)$$ None 0 2
1008.2.bh $$\chi_{1008}(95, \cdot)$$ 1008.2.bh.a 2 2
1008.2.bh.b 2
1008.2.bh.c 30
1008.2.bh.d 30
1008.2.bh.e 32
1008.2.bm $$\chi_{1008}(391, \cdot)$$ None 0 2
1008.2.bn $$\chi_{1008}(103, \cdot)$$ None 0 2
1008.2.bs $$\chi_{1008}(199, \cdot)$$ None 0 2
1008.2.bt $$\chi_{1008}(17, \cdot)$$ 1008.2.bt.a 4 2
1008.2.bt.b 4
1008.2.bt.c 8
1008.2.bt.d 16
1008.2.bu $$\chi_{1008}(359, \cdot)$$ None 0 2
1008.2.bz $$\chi_{1008}(407, \cdot)$$ None 0 2
1008.2.ca $$\chi_{1008}(257, \cdot)$$ 1008.2.ca.a 2 2
1008.2.ca.b 10
1008.2.ca.c 16
1008.2.ca.d 16
1008.2.ca.e 48
1008.2.cb $$\chi_{1008}(23, \cdot)$$ None 0 2
1008.2.cc $$\chi_{1008}(209, \cdot)$$ 1008.2.cc.a 12 2
1008.2.cc.b 16
1008.2.cc.c 16
1008.2.cc.d 48
1008.2.ch $$\chi_{1008}(239, \cdot)$$ 1008.2.ch.a 24 2
1008.2.ch.b 24
1008.2.ch.c 24
1008.2.ci $$\chi_{1008}(761, \cdot)$$ None 0 2
1008.2.cj $$\chi_{1008}(527, \cdot)$$ 1008.2.cj.a 2 2
1008.2.cj.b 2
1008.2.cj.c 30
1008.2.cj.d 30
1008.2.cj.e 32
1008.2.ck $$\chi_{1008}(41, \cdot)$$ None 0 2
1008.2.cp $$\chi_{1008}(89, \cdot)$$ None 0 2
1008.2.cq $$\chi_{1008}(431, \cdot)$$ 1008.2.cq.a 8 2
1008.2.cq.b 12
1008.2.cq.c 12
1008.2.cr $$\chi_{1008}(361, \cdot)$$ None 0 2
1008.2.cs $$\chi_{1008}(271, \cdot)$$ 1008.2.cs.a 2 2
1008.2.cs.b 2
1008.2.cs.c 2
1008.2.cs.d 2
1008.2.cs.e 2
1008.2.cs.f 2
1008.2.cs.g 2
1008.2.cs.h 2
1008.2.cs.i 2
1008.2.cs.j 2
1008.2.cs.k 2
1008.2.cs.l 2
1008.2.cs.m 2
1008.2.cs.n 2
1008.2.cs.o 4
1008.2.cs.p 4
1008.2.cs.q 4
1008.2.cx $$\chi_{1008}(223, \cdot)$$ 1008.2.cx.a 2 2
1008.2.cx.b 2
1008.2.cx.c 2
1008.2.cx.d 2
1008.2.cx.e 2
1008.2.cx.f 2
1008.2.cx.g 2
1008.2.cx.h 2
1008.2.cx.i 24
1008.2.cx.j 24
1008.2.cx.k 32
1008.2.cy $$\chi_{1008}(25, \cdot)$$ None 0 2
1008.2.cz $$\chi_{1008}(367, \cdot)$$ 1008.2.cz.a 2 2
1008.2.cz.b 2
1008.2.cz.c 2
1008.2.cz.d 2
1008.2.cz.e 4
1008.2.cz.f 4
1008.2.cz.g 24
1008.2.cz.h 24
1008.2.cz.i 32
1008.2.da $$\chi_{1008}(169, \cdot)$$ None 0 2
1008.2.df $$\chi_{1008}(689, \cdot)$$ 1008.2.df.a 2 2
1008.2.df.b 10
1008.2.df.c 16
1008.2.df.d 16
1008.2.df.e 48
1008.2.dg $$\chi_{1008}(599, \cdot)$$ None 0 2
1008.2.dh $$\chi_{1008}(439, \cdot)$$ None 0 2
1008.2.dk $$\chi_{1008}(139, \cdot)$$ n/a 752 4
1008.2.dm $$\chi_{1008}(155, \cdot)$$ n/a 576 4
1008.2.do $$\chi_{1008}(205, \cdot)$$ n/a 752 4
1008.2.dr $$\chi_{1008}(5, \cdot)$$ n/a 752 4
1008.2.ds $$\chi_{1008}(269, \cdot)$$ n/a 256 4
1008.2.du $$\chi_{1008}(37, \cdot)$$ n/a 312 4
1008.2.dx $$\chi_{1008}(277, \cdot)$$ n/a 752 4
1008.2.dy $$\chi_{1008}(173, \cdot)$$ n/a 752 4
1008.2.ea $$\chi_{1008}(347, \cdot)$$ n/a 752 4
1008.2.ec $$\chi_{1008}(19, \cdot)$$ n/a 312 4
1008.2.ef $$\chi_{1008}(115, \cdot)$$ n/a 752 4
1008.2.eh $$\chi_{1008}(11, \cdot)$$ n/a 752 4
1008.2.ei $$\chi_{1008}(107, \cdot)$$ n/a 256 4
1008.2.ek $$\chi_{1008}(187, \cdot)$$ n/a 752 4
1008.2.em $$\chi_{1008}(293, \cdot)$$ n/a 752 4
1008.2.eo $$\chi_{1008}(85, \cdot)$$ n/a 576 4

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1008))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1008)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 30}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(252))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(336))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(504))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1008))$$$$^{\oplus 1}$$