# Properties

 Label 2800.2 Level 2800 Weight 2 Dimension 113549 Nonzero newspaces 56 Sturm bound 921600 Trace bound 12

## Defining parameters

 Level: $$N$$ = $$2800 = 2^{4} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$56$$ Sturm bound: $$921600$$ Trace bound: $$12$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2800))$$.

Total New Old
Modular forms 235104 115393 119711
Cusp forms 225697 113549 112148
Eisenstein series 9407 1844 7563

## Trace form

 $$113549 q - 104 q^{2} - 77 q^{3} - 108 q^{4} - 160 q^{5} - 180 q^{6} - 99 q^{7} - 272 q^{8} - 35 q^{9} + O(q^{10})$$ $$113549 q - 104 q^{2} - 77 q^{3} - 108 q^{4} - 160 q^{5} - 180 q^{6} - 99 q^{7} - 272 q^{8} - 35 q^{9} - 128 q^{10} - 133 q^{11} - 100 q^{12} - 150 q^{13} - 128 q^{14} - 264 q^{15} - 156 q^{16} - 267 q^{17} - 112 q^{18} - 139 q^{19} - 128 q^{20} - 313 q^{21} - 264 q^{22} - 147 q^{23} - 108 q^{24} - 48 q^{25} - 340 q^{26} - 110 q^{27} - 76 q^{28} - 346 q^{29} - 64 q^{30} - 89 q^{31} + 36 q^{32} - 155 q^{33} + 140 q^{34} - 108 q^{35} - 160 q^{36} + q^{37} + 140 q^{38} + 26 q^{39} + 32 q^{40} + 82 q^{41} + 100 q^{42} - 148 q^{43} + 172 q^{44} - 100 q^{45} + 120 q^{46} - 95 q^{47} + 252 q^{48} - 231 q^{49} - 240 q^{50} - 291 q^{51} + 136 q^{52} - 131 q^{53} + 252 q^{54} - 124 q^{55} - 120 q^{56} - 122 q^{57} - 181 q^{59} - 192 q^{60} - 195 q^{61} - 32 q^{62} + 7 q^{63} - 276 q^{64} - 344 q^{65} - 316 q^{66} + 95 q^{67} - 272 q^{68} - 74 q^{69} - 232 q^{70} - 124 q^{71} - 500 q^{72} - 131 q^{73} - 460 q^{74} + 160 q^{75} - 612 q^{76} - 197 q^{77} - 800 q^{78} + 253 q^{79} - 288 q^{80} - 400 q^{81} - 364 q^{82} + 344 q^{83} - 428 q^{84} - 192 q^{85} - 428 q^{86} + 602 q^{87} - 476 q^{88} - 3 q^{89} - 368 q^{90} + 84 q^{91} - 388 q^{92} + 61 q^{93} - 372 q^{94} + 236 q^{95} - 516 q^{96} - 54 q^{97} - 244 q^{98} + 556 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2800))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
2800.2.a $$\chi_{2800}(1, \cdot)$$ 2800.2.a.a 1 1
2800.2.a.b 1
2800.2.a.c 1
2800.2.a.d 1
2800.2.a.e 1
2800.2.a.f 1
2800.2.a.g 1
2800.2.a.h 1
2800.2.a.i 1
2800.2.a.j 1
2800.2.a.k 1
2800.2.a.l 1
2800.2.a.m 1
2800.2.a.n 1
2800.2.a.o 1
2800.2.a.p 1
2800.2.a.q 1
2800.2.a.r 1
2800.2.a.s 1
2800.2.a.t 1
2800.2.a.u 1
2800.2.a.v 1
2800.2.a.w 1
2800.2.a.x 1
2800.2.a.y 1
2800.2.a.z 1
2800.2.a.ba 1
2800.2.a.bb 1
2800.2.a.bc 1
2800.2.a.bd 1
2800.2.a.be 1
2800.2.a.bf 1
2800.2.a.bg 1
2800.2.a.bh 2
2800.2.a.bi 2
2800.2.a.bj 2
2800.2.a.bk 2
2800.2.a.bl 2
2800.2.a.bm 2
2800.2.a.bn 2
2800.2.a.bo 2
2800.2.a.bp 2
2800.2.a.bq 3
2800.2.a.br 3
2800.2.b $$\chi_{2800}(1401, \cdot)$$ None 0 1
2800.2.e $$\chi_{2800}(2799, \cdot)$$ 2800.2.e.a 4 1
2800.2.e.b 4
2800.2.e.c 4
2800.2.e.d 4
2800.2.e.e 8
2800.2.e.f 8
2800.2.e.g 8
2800.2.e.h 8
2800.2.e.i 8
2800.2.e.j 8
2800.2.e.k 8
2800.2.g $$\chi_{2800}(449, \cdot)$$ 2800.2.g.a 2 1
2800.2.g.b 2
2800.2.g.c 2
2800.2.g.d 2
2800.2.g.e 2
2800.2.g.f 2
2800.2.g.g 2
2800.2.g.h 2
2800.2.g.i 2
2800.2.g.j 2
2800.2.g.k 2
2800.2.g.l 2
2800.2.g.m 2
2800.2.g.n 2
2800.2.g.o 2
2800.2.g.p 2
2800.2.g.q 2
2800.2.g.r 4
2800.2.g.s 4
2800.2.g.t 4
2800.2.g.u 4
2800.2.g.v 4
2800.2.h $$\chi_{2800}(951, \cdot)$$ None 0 1
2800.2.k $$\chi_{2800}(2351, \cdot)$$ 2800.2.k.a 2 1
2800.2.k.b 2
2800.2.k.c 2
2800.2.k.d 2
2800.2.k.e 2
2800.2.k.f 2
2800.2.k.g 4
2800.2.k.h 4
2800.2.k.i 4
2800.2.k.j 4
2800.2.k.k 8
2800.2.k.l 8
2800.2.k.m 8
2800.2.k.n 8
2800.2.k.o 8
2800.2.k.p 8
2800.2.l $$\chi_{2800}(1849, \cdot)$$ None 0 1
2800.2.n $$\chi_{2800}(1399, \cdot)$$ None 0 1
2800.2.q $$\chi_{2800}(401, \cdot)$$ n/a 146 2
2800.2.r $$\chi_{2800}(293, \cdot)$$ n/a 568 2
2800.2.t $$\chi_{2800}(43, \cdot)$$ n/a 432 2
2800.2.w $$\chi_{2800}(2057, \cdot)$$ None 0 2
2800.2.x $$\chi_{2800}(1807, \cdot)$$ n/a 108 2
2800.2.bb $$\chi_{2800}(1149, \cdot)$$ n/a 432 2
2800.2.bc $$\chi_{2800}(251, \cdot)$$ n/a 596 2
2800.2.bd $$\chi_{2800}(701, \cdot)$$ n/a 456 2
2800.2.be $$\chi_{2800}(699, \cdot)$$ n/a 568 2
2800.2.bi $$\chi_{2800}(407, \cdot)$$ None 0 2
2800.2.bj $$\chi_{2800}(657, \cdot)$$ n/a 140 2
2800.2.bl $$\chi_{2800}(1443, \cdot)$$ n/a 432 2
2800.2.bn $$\chi_{2800}(1693, \cdot)$$ n/a 568 2
2800.2.bp $$\chi_{2800}(561, \cdot)$$ n/a 360 4
2800.2.br $$\chi_{2800}(199, \cdot)$$ None 0 2
2800.2.bt $$\chi_{2800}(1151, \cdot)$$ n/a 152 2
2800.2.bw $$\chi_{2800}(249, \cdot)$$ None 0 2
2800.2.bx $$\chi_{2800}(849, \cdot)$$ n/a 140 2
2800.2.ca $$\chi_{2800}(551, \cdot)$$ None 0 2
2800.2.cc $$\chi_{2800}(1801, \cdot)$$ None 0 2
2800.2.cd $$\chi_{2800}(1599, \cdot)$$ n/a 144 2
2800.2.ch $$\chi_{2800}(279, \cdot)$$ None 0 4
2800.2.cj $$\chi_{2800}(169, \cdot)$$ None 0 4
2800.2.ck $$\chi_{2800}(111, \cdot)$$ n/a 480 4
2800.2.cn $$\chi_{2800}(391, \cdot)$$ None 0 4
2800.2.co $$\chi_{2800}(1009, \cdot)$$ n/a 360 4
2800.2.cq $$\chi_{2800}(559, \cdot)$$ n/a 480 4
2800.2.ct $$\chi_{2800}(281, \cdot)$$ None 0 4
2800.2.cv $$\chi_{2800}(107, \cdot)$$ n/a 1136 4
2800.2.cx $$\chi_{2800}(493, \cdot)$$ n/a 1136 4
2800.2.cy $$\chi_{2800}(257, \cdot)$$ n/a 280 4
2800.2.db $$\chi_{2800}(807, \cdot)$$ None 0 4
2800.2.de $$\chi_{2800}(299, \cdot)$$ n/a 1136 4
2800.2.df $$\chi_{2800}(501, \cdot)$$ n/a 1192 4
2800.2.dg $$\chi_{2800}(451, \cdot)$$ n/a 1192 4
2800.2.dh $$\chi_{2800}(149, \cdot)$$ n/a 1136 4
2800.2.dk $$\chi_{2800}(207, \cdot)$$ n/a 288 4
2800.2.dn $$\chi_{2800}(857, \cdot)$$ None 0 4
2800.2.dp $$\chi_{2800}(157, \cdot)$$ n/a 1136 4
2800.2.dr $$\chi_{2800}(443, \cdot)$$ n/a 1136 4
2800.2.ds $$\chi_{2800}(81, \cdot)$$ n/a 944 8
2800.2.du $$\chi_{2800}(13, \cdot)$$ n/a 3808 8
2800.2.dw $$\chi_{2800}(267, \cdot)$$ n/a 2880 8
2800.2.dy $$\chi_{2800}(97, \cdot)$$ n/a 944 8
2800.2.dz $$\chi_{2800}(183, \cdot)$$ None 0 8
2800.2.ed $$\chi_{2800}(139, \cdot)$$ n/a 3808 8
2800.2.ee $$\chi_{2800}(141, \cdot)$$ n/a 2880 8
2800.2.ef $$\chi_{2800}(531, \cdot)$$ n/a 3808 8
2800.2.eg $$\chi_{2800}(29, \cdot)$$ n/a 2880 8
2800.2.ek $$\chi_{2800}(127, \cdot)$$ n/a 720 8
2800.2.el $$\chi_{2800}(153, \cdot)$$ None 0 8
2800.2.eo $$\chi_{2800}(547, \cdot)$$ n/a 2880 8
2800.2.eq $$\chi_{2800}(237, \cdot)$$ n/a 3808 8
2800.2.es $$\chi_{2800}(159, \cdot)$$ n/a 960 8
2800.2.et $$\chi_{2800}(121, \cdot)$$ None 0 8
2800.2.ev $$\chi_{2800}(311, \cdot)$$ None 0 8
2800.2.ey $$\chi_{2800}(289, \cdot)$$ n/a 944 8
2800.2.ez $$\chi_{2800}(9, \cdot)$$ None 0 8
2800.2.fc $$\chi_{2800}(31, \cdot)$$ n/a 960 8
2800.2.fe $$\chi_{2800}(439, \cdot)$$ None 0 8
2800.2.fg $$\chi_{2800}(67, \cdot)$$ n/a 7616 16
2800.2.fi $$\chi_{2800}(213, \cdot)$$ n/a 7616 16
2800.2.fk $$\chi_{2800}(73, \cdot)$$ None 0 16
2800.2.fn $$\chi_{2800}(303, \cdot)$$ n/a 1920 16
2800.2.fq $$\chi_{2800}(109, \cdot)$$ n/a 7616 16
2800.2.fr $$\chi_{2800}(131, \cdot)$$ n/a 7616 16
2800.2.fs $$\chi_{2800}(221, \cdot)$$ n/a 7616 16
2800.2.ft $$\chi_{2800}(19, \cdot)$$ n/a 7616 16
2800.2.fw $$\chi_{2800}(23, \cdot)$$ None 0 16
2800.2.fz $$\chi_{2800}(17, \cdot)$$ n/a 1888 16
2800.2.ga $$\chi_{2800}(117, \cdot)$$ n/a 7616 16
2800.2.gc $$\chi_{2800}(163, \cdot)$$ n/a 7616 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2800))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2800)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(140))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(200))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(280))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(350))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(400))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(560))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(700))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1400))$$$$^{\oplus 2}$$