# Properties

 Label 1008.3 Level 1008 Weight 3 Dimension 23395 Nonzero newspaces 40 Sturm bound 165888 Trace bound 29

## Defining parameters

 Level: $$N$$ = $$1008 = 2^{4} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$40$$ Sturm bound: $$165888$$ Trace bound: $$29$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(1008))$$.

Total New Old
Modular forms 56640 23801 32839
Cusp forms 53952 23395 30557
Eisenstein series 2688 406 2282

## Trace form

 $$23395 q - 24 q^{2} - 24 q^{3} - 12 q^{4} - 15 q^{5} - 32 q^{6} - 4 q^{7} - 72 q^{8} + 8 q^{9} + O(q^{10})$$ $$23395 q - 24 q^{2} - 24 q^{3} - 12 q^{4} - 15 q^{5} - 32 q^{6} - 4 q^{7} - 72 q^{8} + 8 q^{9} - 148 q^{10} + 11 q^{11} - 32 q^{12} - 80 q^{13} - 76 q^{14} - 126 q^{15} - 172 q^{16} - 285 q^{17} - 232 q^{18} - 197 q^{19} - 196 q^{20} - 91 q^{21} - 56 q^{22} - 89 q^{23} + 32 q^{24} + 197 q^{25} + 164 q^{26} - 168 q^{27} + 92 q^{28} + 140 q^{29} + 392 q^{30} + 91 q^{31} + 676 q^{32} + 42 q^{33} + 476 q^{34} - 267 q^{35} + 312 q^{36} - 359 q^{37} + 900 q^{38} - 294 q^{39} + 788 q^{40} - 48 q^{41} + 160 q^{42} - 692 q^{43} - 68 q^{44} + 282 q^{45} - 608 q^{46} + 279 q^{47} - 136 q^{48} + 42 q^{49} - 1136 q^{50} + 604 q^{51} - 1192 q^{52} + 107 q^{53} - 648 q^{54} + 796 q^{55} - 304 q^{56} + 608 q^{57} - 1248 q^{58} + 1243 q^{59} + 1000 q^{60} + 77 q^{61} + 1152 q^{62} + 303 q^{63} - 564 q^{64} + 292 q^{65} + 1168 q^{66} + 39 q^{67} + 584 q^{68} - 526 q^{69} + 656 q^{70} - 718 q^{71} - 256 q^{72} - 455 q^{73} - 180 q^{74} - 776 q^{75} + 828 q^{76} - 1082 q^{77} - 1160 q^{78} + 595 q^{79} + 348 q^{80} - 1592 q^{81} + 2980 q^{82} + 548 q^{83} - 568 q^{84} - 418 q^{85} + 108 q^{86} + 534 q^{87} + 1652 q^{88} + 3 q^{89} - 608 q^{90} + 50 q^{91} + 1156 q^{92} - 234 q^{93} + 1356 q^{94} - 951 q^{95} - 168 q^{96} + 72 q^{97} + 512 q^{98} - 414 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(1008))$$

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
1008.3.d $$\chi_{1008}(449, \cdot)$$ 1008.3.d.a 4 1
1008.3.d.b 4
1008.3.d.c 4
1008.3.d.d 4
1008.3.d.e 8
1008.3.e $$\chi_{1008}(503, \cdot)$$ None 0 1
1008.3.f $$\chi_{1008}(433, \cdot)$$ 1008.3.f.a 1 1
1008.3.f.b 2
1008.3.f.c 2
1008.3.f.d 2
1008.3.f.e 2
1008.3.f.f 2
1008.3.f.g 4
1008.3.f.h 4
1008.3.f.i 4
1008.3.f.j 8
1008.3.f.k 8
1008.3.g $$\chi_{1008}(631, \cdot)$$ None 0 1
1008.3.l $$\chi_{1008}(937, \cdot)$$ None 0 1
1008.3.m $$\chi_{1008}(127, \cdot)$$ 1008.3.m.a 2 1
1008.3.m.b 4
1008.3.m.c 4
1008.3.m.d 4
1008.3.m.e 4
1008.3.m.f 4
1008.3.m.g 8
1008.3.n $$\chi_{1008}(953, \cdot)$$ None 0 1
1008.3.o $$\chi_{1008}(1007, \cdot)$$ 1008.3.o.a 8 1
1008.3.o.b 24
1008.3.u $$\chi_{1008}(181, \cdot)$$ n/a 316 2
1008.3.w $$\chi_{1008}(197, \cdot)$$ n/a 192 2
1008.3.y $$\chi_{1008}(251, \cdot)$$ n/a 256 2
1008.3.ba $$\chi_{1008}(379, \cdot)$$ n/a 240 2
1008.3.bc $$\chi_{1008}(311, \cdot)$$ None 0 2
1008.3.bd $$\chi_{1008}(65, \cdot)$$ n/a 188 2
1008.3.bi $$\chi_{1008}(583, \cdot)$$ None 0 2
1008.3.bj $$\chi_{1008}(817, \cdot)$$ n/a 188 2
1008.3.bk $$\chi_{1008}(143, \cdot)$$ 1008.3.bk.a 20 2
1008.3.bk.b 20
1008.3.bk.c 24
1008.3.bl $$\chi_{1008}(233, \cdot)$$ None 0 2
1008.3.bo $$\chi_{1008}(281, \cdot)$$ None 0 2
1008.3.bp $$\chi_{1008}(383, \cdot)$$ n/a 192 2
1008.3.bq $$\chi_{1008}(137, \cdot)$$ None 0 2
1008.3.br $$\chi_{1008}(335, \cdot)$$ n/a 192 2
1008.3.bv $$\chi_{1008}(265, \cdot)$$ None 0 2
1008.3.bw $$\chi_{1008}(655, \cdot)$$ n/a 192 2
1008.3.bx $$\chi_{1008}(745, \cdot)$$ None 0 2
1008.3.by $$\chi_{1008}(463, \cdot)$$ n/a 144 2
1008.3.cd $$\chi_{1008}(415, \cdot)$$ 1008.3.cd.a 2 2
1008.3.cd.b 2
1008.3.cd.c 2
1008.3.cd.d 2
1008.3.cd.e 4
1008.3.cd.f 4
1008.3.cd.g 4
1008.3.cd.h 6
1008.3.cd.i 6
1008.3.cd.j 6
1008.3.cd.k 6
1008.3.cd.l 6
1008.3.cd.m 6
1008.3.cd.n 8
1008.3.cd.o 8
1008.3.cd.p 8
1008.3.ce $$\chi_{1008}(73, \cdot)$$ None 0 2
1008.3.cf $$\chi_{1008}(487, \cdot)$$ None 0 2
1008.3.cg $$\chi_{1008}(145, \cdot)$$ 1008.3.cg.a 2 2
1008.3.cg.b 2
1008.3.cg.c 2
1008.3.cg.d 2
1008.3.cg.e 2
1008.3.cg.f 2
1008.3.cg.g 2
1008.3.cg.h 4
1008.3.cg.i 4
1008.3.cg.j 4
1008.3.cg.k 4
1008.3.cg.l 4
1008.3.cg.m 4
1008.3.cg.n 8
1008.3.cg.o 8
1008.3.cg.p 8
1008.3.cg.q 16
1008.3.cl $$\chi_{1008}(97, \cdot)$$ n/a 188 2
1008.3.cm $$\chi_{1008}(151, \cdot)$$ None 0 2
1008.3.cn $$\chi_{1008}(241, \cdot)$$ n/a 188 2
1008.3.co $$\chi_{1008}(295, \cdot)$$ None 0 2
1008.3.ct $$\chi_{1008}(113, \cdot)$$ n/a 144 2
1008.3.cu $$\chi_{1008}(887, \cdot)$$ None 0 2
1008.3.cv $$\chi_{1008}(401, \cdot)$$ n/a 188 2
1008.3.cw $$\chi_{1008}(167, \cdot)$$ None 0 2
1008.3.db $$\chi_{1008}(215, \cdot)$$ None 0 2
1008.3.dc $$\chi_{1008}(305, \cdot)$$ 1008.3.dc.a 4 2
1008.3.dc.b 4
1008.3.dc.c 4
1008.3.dc.d 8
1008.3.dc.e 12
1008.3.dc.f 16
1008.3.dc.g 16
1008.3.dd $$\chi_{1008}(79, \cdot)$$ n/a 192 2
1008.3.de $$\chi_{1008}(313, \cdot)$$ None 0 2
1008.3.di $$\chi_{1008}(47, \cdot)$$ n/a 192 2
1008.3.dj $$\chi_{1008}(473, \cdot)$$ None 0 2
1008.3.dl $$\chi_{1008}(29, \cdot)$$ n/a 1152 4
1008.3.dn $$\chi_{1008}(13, \cdot)$$ n/a 1520 4
1008.3.dp $$\chi_{1008}(59, \cdot)$$ n/a 1520 4
1008.3.dq $$\chi_{1008}(403, \cdot)$$ n/a 1520 4
1008.3.dt $$\chi_{1008}(163, \cdot)$$ n/a 632 4
1008.3.dv $$\chi_{1008}(395, \cdot)$$ n/a 512 4
1008.3.dw $$\chi_{1008}(131, \cdot)$$ n/a 1520 4
1008.3.dz $$\chi_{1008}(67, \cdot)$$ n/a 1520 4
1008.3.eb $$\chi_{1008}(61, \cdot)$$ n/a 1520 4
1008.3.ed $$\chi_{1008}(53, \cdot)$$ n/a 512 4
1008.3.ee $$\chi_{1008}(149, \cdot)$$ n/a 1520 4
1008.3.eg $$\chi_{1008}(229, \cdot)$$ n/a 1520 4
1008.3.ej $$\chi_{1008}(325, \cdot)$$ n/a 632 4
1008.3.el $$\chi_{1008}(221, \cdot)$$ n/a 1520 4
1008.3.en $$\chi_{1008}(43, \cdot)$$ n/a 1152 4
1008.3.ep $$\chi_{1008}(83, \cdot)$$ n/a 1520 4

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

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(1008))$$ into lower level spaces

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