# Properties

 Label 2736.3 Level 2736 Weight 3 Dimension 182965 Nonzero newspaces 64 Sturm bound 1244160 Trace bound 33

## Defining parameters

 Level: $$N$$ = $$2736 = 2^{4} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$64$$ Sturm bound: $$1244160$$ Trace bound: $$33$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(2736))$$.

Total New Old
Modular forms 418752 184343 234409
Cusp forms 410688 182965 227723
Eisenstein series 8064 1378 6686

## Trace form

 $$182965 q - 96 q^{2} - 96 q^{3} - 84 q^{4} - 105 q^{5} - 128 q^{6} - 35 q^{7} - 108 q^{8} - 16 q^{9} + O(q^{10})$$ $$182965 q - 96 q^{2} - 96 q^{3} - 84 q^{4} - 105 q^{5} - 128 q^{6} - 35 q^{7} - 108 q^{8} - 16 q^{9} - 364 q^{10} - 43 q^{11} - 128 q^{12} - 173 q^{13} - 188 q^{14} - 162 q^{15} - 244 q^{16} - 447 q^{17} - 328 q^{18} - 325 q^{19} - 376 q^{20} - 242 q^{21} - 92 q^{22} - 215 q^{23} - 64 q^{24} + 131 q^{25} + 92 q^{26} - 240 q^{27} + 76 q^{28} + 119 q^{29} + 296 q^{30} + 133 q^{31} + 604 q^{32} - 174 q^{33} + 404 q^{34} - 273 q^{35} + 264 q^{36} - 500 q^{37} + 360 q^{38} - 474 q^{39} + 716 q^{40} - 57 q^{41} + 272 q^{42} - 647 q^{43} + 388 q^{44} + 162 q^{45} - 284 q^{46} + 369 q^{47} - 232 q^{48} - 9 q^{49} - 752 q^{50} + 532 q^{51} - 940 q^{52} + 113 q^{53} - 744 q^{54} + 649 q^{55} - 812 q^{56} + 280 q^{57} - 1680 q^{58} + 1093 q^{59} + 904 q^{60} + 203 q^{61} + 324 q^{62} + 570 q^{63} - 1428 q^{64} + 595 q^{65} + 1072 q^{66} + 921 q^{67} - 268 q^{68} + 26 q^{69} - 164 q^{70} + 671 q^{71} - 352 q^{72} + 427 q^{73} - 252 q^{74} + 16 q^{75} + 324 q^{76} - 832 q^{77} - 1208 q^{78} + 541 q^{79} + 276 q^{80} - 1616 q^{81} + 2764 q^{82} + 53 q^{83} - 1184 q^{84} - 1471 q^{85} + 36 q^{86} + 30 q^{87} + 1580 q^{88} - 1887 q^{89} - 704 q^{90} - 1679 q^{91} + 892 q^{92} - 1314 q^{93} + 60 q^{94} - 795 q^{95} - 408 q^{96} - 1101 q^{97} - 1784 q^{98} - 1602 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(2736))$$

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
2736.3.b $$\chi_{2736}(2735, \cdot)$$ 2736.3.b.a 8 1
2736.3.b.b 8
2736.3.b.c 16
2736.3.b.d 16
2736.3.b.e 32
2736.3.c $$\chi_{2736}(343, \cdot)$$ None 0 1
2736.3.h $$\chi_{2736}(305, \cdot)$$ 2736.3.h.a 4 1
2736.3.h.b 8
2736.3.h.c 12
2736.3.h.d 12
2736.3.h.e 16
2736.3.h.f 20
2736.3.i $$\chi_{2736}(2089, \cdot)$$ None 0 1
2736.3.l $$\chi_{2736}(1367, \cdot)$$ None 0 1
2736.3.m $$\chi_{2736}(1711, \cdot)$$ 2736.3.m.a 6 1
2736.3.m.b 12
2736.3.m.c 12
2736.3.m.d 12
2736.3.m.e 12
2736.3.m.f 12
2736.3.m.g 24
2736.3.n $$\chi_{2736}(1673, \cdot)$$ None 0 1
2736.3.o $$\chi_{2736}(721, \cdot)$$ 2736.3.o.a 1 1
2736.3.o.b 2
2736.3.o.c 2
2736.3.o.d 2
2736.3.o.e 2
2736.3.o.f 2
2736.3.o.g 2
2736.3.o.h 2
2736.3.o.i 2
2736.3.o.j 4
2736.3.o.k 4
2736.3.o.l 4
2736.3.o.m 6
2736.3.o.n 8
2736.3.o.o 8
2736.3.o.p 8
2736.3.o.q 20
2736.3.o.r 20
2736.3.v $$\chi_{2736}(989, \cdot)$$ n/a 576 2
2736.3.w $$\chi_{2736}(37, \cdot)$$ n/a 796 2
2736.3.z $$\chi_{2736}(683, \cdot)$$ n/a 640 2
2736.3.ba $$\chi_{2736}(1027, \cdot)$$ n/a 720 2
2736.3.bc $$\chi_{2736}(2041, \cdot)$$ None 0 2
2736.3.bd $$\chi_{2736}(353, \cdot)$$ n/a 476 2
2736.3.bi $$\chi_{2736}(1303, \cdot)$$ None 0 2
2736.3.bj $$\chi_{2736}(1247, \cdot)$$ n/a 480 2
2736.3.bk $$\chi_{2736}(847, \cdot)$$ n/a 200 2
2736.3.bl $$\chi_{2736}(791, \cdot)$$ None 0 2
2736.3.bo $$\chi_{2736}(1969, \cdot)$$ n/a 476 2
2736.3.bp $$\chi_{2736}(425, \cdot)$$ None 0 2
2736.3.br $$\chi_{2736}(761, \cdot)$$ None 0 2
2736.3.bs $$\chi_{2736}(1633, \cdot)$$ n/a 476 2
2736.3.bw $$\chi_{2736}(455, \cdot)$$ None 0 2
2736.3.bx $$\chi_{2736}(799, \cdot)$$ n/a 432 2
2736.3.ca $$\chi_{2736}(1375, \cdot)$$ n/a 480 2
2736.3.cb $$\chi_{2736}(1319, \cdot)$$ None 0 2
2736.3.cd $$\chi_{2736}(145, \cdot)$$ n/a 198 2
2736.3.ce $$\chi_{2736}(809, \cdot)$$ None 0 2
2736.3.ch $$\chi_{2736}(919, \cdot)$$ None 0 2
2736.3.ci $$\chi_{2736}(863, \cdot)$$ n/a 160 2
2736.3.cl $$\chi_{2736}(1217, \cdot)$$ n/a 432 2
2736.3.cm $$\chi_{2736}(265, \cdot)$$ None 0 2
2736.3.cp $$\chi_{2736}(601, \cdot)$$ None 0 2
2736.3.cq $$\chi_{2736}(1265, \cdot)$$ n/a 476 2
2736.3.cr $$\chi_{2736}(7, \cdot)$$ None 0 2
2736.3.cs $$\chi_{2736}(335, \cdot)$$ n/a 480 2
2736.3.cv $$\chi_{2736}(911, \cdot)$$ n/a 480 2
2736.3.cw $$\chi_{2736}(1255, \cdot)$$ None 0 2
2736.3.cz $$\chi_{2736}(217, \cdot)$$ None 0 2
2736.3.da $$\chi_{2736}(881, \cdot)$$ n/a 160 2
2736.3.de $$\chi_{2736}(673, \cdot)$$ n/a 476 2
2736.3.df $$\chi_{2736}(1337, \cdot)$$ None 0 2
2736.3.dg $$\chi_{2736}(463, \cdot)$$ n/a 480 2
2736.3.dh $$\chi_{2736}(407, \cdot)$$ None 0 2
2736.3.dn $$\chi_{2736}(829, \cdot)$$ n/a 1592 4
2736.3.dq $$\chi_{2736}(125, \cdot)$$ n/a 1280 4
2736.3.dr $$\chi_{2736}(227, \cdot)$$ n/a 3824 4
2736.3.du $$\chi_{2736}(619, \cdot)$$ n/a 3824 4
2736.3.dw $$\chi_{2736}(691, \cdot)$$ n/a 3824 4
2736.3.dx $$\chi_{2736}(635, \cdot)$$ n/a 3824 4
2736.3.dz $$\chi_{2736}(563, \cdot)$$ n/a 3824 4
2736.3.ec $$\chi_{2736}(115, \cdot)$$ n/a 3456 4
2736.3.ed $$\chi_{2736}(77, \cdot)$$ n/a 3456 4
2736.3.eg $$\chi_{2736}(445, \cdot)$$ n/a 3824 4
2736.3.ei $$\chi_{2736}(373, \cdot)$$ n/a 3824 4
2736.3.ej $$\chi_{2736}(653, \cdot)$$ n/a 3824 4
2736.3.el $$\chi_{2736}(581, \cdot)$$ n/a 3824 4
2736.3.eo $$\chi_{2736}(493, \cdot)$$ n/a 3824 4
2736.3.ep $$\chi_{2736}(163, \cdot)$$ n/a 1592 4
2736.3.es $$\chi_{2736}(107, \cdot)$$ n/a 1280 4
2736.3.et $$\chi_{2736}(1199, \cdot)$$ n/a 1440 6
2736.3.ev $$\chi_{2736}(727, \cdot)$$ None 0 6
2736.3.ey $$\chi_{2736}(167, \cdot)$$ None 0 6
2736.3.fa $$\chi_{2736}(175, \cdot)$$ n/a 1440 6
2736.3.fc $$\chi_{2736}(553, \cdot)$$ None 0 6
2736.3.fe $$\chi_{2736}(689, \cdot)$$ n/a 1428 6
2736.3.ff $$\chi_{2736}(233, \cdot)$$ None 0 6
2736.3.fg $$\chi_{2736}(433, \cdot)$$ n/a 594 6
2736.3.fj $$\chi_{2736}(17, \cdot)$$ n/a 480 6
2736.3.fl $$\chi_{2736}(649, \cdot)$$ None 0 6
2736.3.fm $$\chi_{2736}(193, \cdot)$$ n/a 1428 6
2736.3.fo $$\chi_{2736}(137, \cdot)$$ None 0 6
2736.3.fq $$\chi_{2736}(367, \cdot)$$ n/a 1440 6
2736.3.fs $$\chi_{2736}(743, \cdot)$$ None 0 6
2736.3.ft $$\chi_{2736}(143, \cdot)$$ n/a 480 6
2736.3.fv $$\chi_{2736}(55, \cdot)$$ None 0 6
2736.3.fy $$\chi_{2736}(71, \cdot)$$ None 0 6
2736.3.ga $$\chi_{2736}(271, \cdot)$$ n/a 600 6
2736.3.gb $$\chi_{2736}(967, \cdot)$$ None 0 6
2736.3.gd $$\chi_{2736}(383, \cdot)$$ n/a 1440 6
2736.3.gf $$\chi_{2736}(329, \cdot)$$ None 0 6
2736.3.gg $$\chi_{2736}(97, \cdot)$$ n/a 1428 6
2736.3.gj $$\chi_{2736}(929, \cdot)$$ n/a 1428 6
2736.3.gl $$\chi_{2736}(409, \cdot)$$ None 0 6
2736.3.gn $$\chi_{2736}(245, \cdot)$$ n/a 11472 12
2736.3.gp $$\chi_{2736}(13, \cdot)$$ n/a 11472 12
2736.3.gr $$\chi_{2736}(283, \cdot)$$ n/a 11472 12
2736.3.gs $$\chi_{2736}(395, \cdot)$$ n/a 3840 12
2736.3.gu $$\chi_{2736}(595, \cdot)$$ n/a 4776 12
2736.3.gx $$\chi_{2736}(59, \cdot)$$ n/a 11472 12
2736.3.gy $$\chi_{2736}(205, \cdot)$$ n/a 11472 12
2736.3.hb $$\chi_{2736}(557, \cdot)$$ n/a 3840 12
2736.3.hd $$\chi_{2736}(109, \cdot)$$ n/a 4776 12
2736.3.he $$\chi_{2736}(5, \cdot)$$ n/a 11472 12
2736.3.hg $$\chi_{2736}(155, \cdot)$$ n/a 11472 12
2736.3.hi $$\chi_{2736}(43, \cdot)$$ n/a 11472 12

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

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(2736))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(2736)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 15}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(171))$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(228))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(342))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(456))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(684))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(912))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(1368))$$$$^{\oplus 2}$$