# Properties

 Label 1248.2 Level 1248 Weight 2 Dimension 17708 Nonzero newspaces 40 Sturm bound 172032 Trace bound 28

## Defining parameters

 Level: $$N$$ = $$1248 = 2^{5} \cdot 3 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$172032$$ Trace bound: $$28$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1248))$$.

Total New Old
Modular forms 44544 18148 26396
Cusp forms 41473 17708 23765
Eisenstein series 3071 440 2631

## Trace form

 $$17708 q - 32 q^{3} - 80 q^{4} - 8 q^{5} - 40 q^{6} - 64 q^{7} - 68 q^{9} + O(q^{10})$$ $$17708 q - 32 q^{3} - 80 q^{4} - 8 q^{5} - 40 q^{6} - 64 q^{7} - 68 q^{9} - 48 q^{10} - 8 q^{12} - 76 q^{13} + 64 q^{14} - 12 q^{15} + 32 q^{17} - 24 q^{18} - 48 q^{19} + 64 q^{20} - 8 q^{21} - 32 q^{22} + 48 q^{23} - 64 q^{24} - 84 q^{25} - 40 q^{26} + 4 q^{27} - 160 q^{28} - 8 q^{29} - 136 q^{30} + 32 q^{31} - 80 q^{32} - 104 q^{33} - 128 q^{34} + 96 q^{35} - 144 q^{36} - 120 q^{37} - 80 q^{38} - 16 q^{39} - 256 q^{40} - 16 q^{41} - 160 q^{42} - 64 q^{43} - 16 q^{44} - 112 q^{45} - 80 q^{46} - 48 q^{47} - 144 q^{48} - 124 q^{49} - 48 q^{50} - 56 q^{51} - 136 q^{52} + 24 q^{53} - 144 q^{54} - 184 q^{55} - 112 q^{56} - 104 q^{57} - 224 q^{58} - 128 q^{59} - 160 q^{60} + 40 q^{61} - 96 q^{62} - 60 q^{63} - 224 q^{64} - 8 q^{65} - 136 q^{66} - 160 q^{67} + 16 q^{68} + 88 q^{69} - 128 q^{70} - 80 q^{71} + 80 q^{72} - 40 q^{73} + 64 q^{74} - 76 q^{75} - 80 q^{76} + 128 q^{77} + 20 q^{78} - 136 q^{79} + 112 q^{80} + 52 q^{81} + 80 q^{82} + 224 q^{84} + 96 q^{85} + 128 q^{86} - 92 q^{87} + 96 q^{88} + 192 q^{89} + 224 q^{90} + 128 q^{91} + 160 q^{92} + 128 q^{93} + 96 q^{94} + 208 q^{95} + 240 q^{96} + 8 q^{97} + 160 q^{98} + 4 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1248))$$

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
1248.2.a $$\chi_{1248}(1, \cdot)$$ 1248.2.a.a 1 1
1248.2.a.b 1
1248.2.a.c 1
1248.2.a.d 1
1248.2.a.e 1
1248.2.a.f 1
1248.2.a.g 1
1248.2.a.h 1
1248.2.a.i 1
1248.2.a.j 1
1248.2.a.k 2
1248.2.a.l 2
1248.2.a.m 2
1248.2.a.n 2
1248.2.a.o 3
1248.2.a.p 3
1248.2.c $$\chi_{1248}(961, \cdot)$$ 1248.2.c.a 6 1
1248.2.c.b 6
1248.2.c.c 8
1248.2.c.d 8
1248.2.d $$\chi_{1248}(287, \cdot)$$ 1248.2.d.a 4 1
1248.2.d.b 8
1248.2.d.c 16
1248.2.d.d 20
1248.2.g $$\chi_{1248}(625, \cdot)$$ 1248.2.g.a 8 1
1248.2.g.b 16
1248.2.h $$\chi_{1248}(623, \cdot)$$ 1248.2.h.a 8 1
1248.2.h.b 12
1248.2.h.c 32
1248.2.j $$\chi_{1248}(911, \cdot)$$ 1248.2.j.a 48 1
1248.2.m $$\chi_{1248}(337, \cdot)$$ 1248.2.m.a 2 1
1248.2.m.b 2
1248.2.m.c 24
1248.2.n $$\chi_{1248}(1247, \cdot)$$ 1248.2.n.a 4 1
1248.2.n.b 4
1248.2.n.c 4
1248.2.n.d 4
1248.2.n.e 40
1248.2.q $$\chi_{1248}(289, \cdot)$$ 1248.2.q.a 2 2
1248.2.q.b 2
1248.2.q.c 2
1248.2.q.d 2
1248.2.q.e 2
1248.2.q.f 2
1248.2.q.g 4
1248.2.q.h 4
1248.2.q.i 4
1248.2.q.j 4
1248.2.q.k 6
1248.2.q.l 6
1248.2.q.m 8
1248.2.q.n 8
1248.2.r $$\chi_{1248}(343, \cdot)$$ None 0 2
1248.2.u $$\chi_{1248}(473, \cdot)$$ None 0 2
1248.2.v $$\chi_{1248}(311, \cdot)$$ None 0 2
1248.2.x $$\chi_{1248}(313, \cdot)$$ None 0 2
1248.2.bb $$\chi_{1248}(463, \cdot)$$ 1248.2.bb.a 2 2
1248.2.bb.b 2
1248.2.bb.c 2
1248.2.bb.d 2
1248.2.bb.e 24
1248.2.bb.f 24
1248.2.bc $$\chi_{1248}(31, \cdot)$$ 1248.2.bc.a 2 2
1248.2.bc.b 2
1248.2.bc.c 2
1248.2.bc.d 2
1248.2.bc.e 2
1248.2.bc.f 2
1248.2.bc.g 2
1248.2.bc.h 2
1248.2.bc.i 2
1248.2.bc.j 2
1248.2.bc.k 2
1248.2.bc.l 2
1248.2.bc.m 2
1248.2.bc.n 2
1248.2.bc.o 4
1248.2.bc.p 4
1248.2.bc.q 4
1248.2.bc.r 4
1248.2.bc.s 6
1248.2.bc.t 6
1248.2.bf $$\chi_{1248}(161, \cdot)$$ n/a 112 2
1248.2.bg $$\chi_{1248}(593, \cdot)$$ n/a 104 2
1248.2.bh $$\chi_{1248}(599, \cdot)$$ None 0 2
1248.2.bj $$\chi_{1248}(25, \cdot)$$ None 0 2
1248.2.bm $$\chi_{1248}(281, \cdot)$$ None 0 2
1248.2.bn $$\chi_{1248}(151, \cdot)$$ None 0 2
1248.2.bq $$\chi_{1248}(335, \cdot)$$ n/a 104 2
1248.2.br $$\chi_{1248}(529, \cdot)$$ 1248.2.br.a 56 2
1248.2.bu $$\chi_{1248}(191, \cdot)$$ n/a 112 2
1248.2.bv $$\chi_{1248}(673, \cdot)$$ 1248.2.bv.a 12 2
1248.2.bv.b 12
1248.2.bv.c 16
1248.2.bv.d 16
1248.2.bz $$\chi_{1248}(95, \cdot)$$ n/a 112 2
1248.2.ca $$\chi_{1248}(49, \cdot)$$ 1248.2.ca.a 8 2
1248.2.ca.b 48
1248.2.cd $$\chi_{1248}(815, \cdot)$$ n/a 104 2
1248.2.cf $$\chi_{1248}(5, \cdot)$$ n/a 880 4
1248.2.ch $$\chi_{1248}(499, \cdot)$$ n/a 448 4
1248.2.ci $$\chi_{1248}(181, \cdot)$$ n/a 448 4
1248.2.ck $$\chi_{1248}(157, \cdot)$$ n/a 384 4
1248.2.cn $$\chi_{1248}(131, \cdot)$$ n/a 768 4
1248.2.cp $$\chi_{1248}(155, \cdot)$$ n/a 880 4
1248.2.cq $$\chi_{1248}(317, \cdot)$$ n/a 880 4
1248.2.cs $$\chi_{1248}(187, \cdot)$$ n/a 448 4
1248.2.cu $$\chi_{1248}(137, \cdot)$$ None 0 4
1248.2.cx $$\chi_{1248}(7, \cdot)$$ None 0 4
1248.2.cz $$\chi_{1248}(121, \cdot)$$ None 0 4
1248.2.db $$\chi_{1248}(263, \cdot)$$ None 0 4
1248.2.dc $$\chi_{1248}(305, \cdot)$$ n/a 208 4
1248.2.dd $$\chi_{1248}(353, \cdot)$$ n/a 224 4
1248.2.dg $$\chi_{1248}(223, \cdot)$$ n/a 112 4
1248.2.dh $$\chi_{1248}(175, \cdot)$$ n/a 112 4
1248.2.dl $$\chi_{1248}(217, \cdot)$$ None 0 4
1248.2.dn $$\chi_{1248}(23, \cdot)$$ None 0 4
1248.2.dp $$\chi_{1248}(487, \cdot)$$ None 0 4
1248.2.dq $$\chi_{1248}(41, \cdot)$$ None 0 4
1248.2.dt $$\chi_{1248}(115, \cdot)$$ n/a 896 8
1248.2.dv $$\chi_{1248}(245, \cdot)$$ n/a 1760 8
1248.2.dx $$\chi_{1248}(35, \cdot)$$ n/a 1760 8
1248.2.dz $$\chi_{1248}(179, \cdot)$$ n/a 1760 8
1248.2.ea $$\chi_{1248}(205, \cdot)$$ n/a 896 8
1248.2.ec $$\chi_{1248}(61, \cdot)$$ n/a 896 8
1248.2.ee $$\chi_{1248}(19, \cdot)$$ n/a 896 8
1248.2.eg $$\chi_{1248}(149, \cdot)$$ n/a 1760 8

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1248))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1248)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(208))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(416))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(624))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1248))$$$$^{\oplus 1}$$