# Properties

 Label 2200.2 Level 2200 Weight 2 Dimension 72673 Nonzero newspaces 63 Sturm bound 576000 Trace bound 27

## Defining parameters

 Level: $$N$$ = $$2200 = 2^{3} \cdot 5^{2} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$63$$ Sturm bound: $$576000$$ Trace bound: $$27$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2200))$$.

Total New Old
Modular forms 147360 74149 73211
Cusp forms 140641 72673 67968
Eisenstein series 6719 1476 5243

## Trace form

 $$72673 q - 106 q^{2} - 106 q^{3} - 106 q^{4} - 2 q^{5} - 170 q^{6} - 122 q^{7} - 106 q^{8} - 232 q^{9} + O(q^{10})$$ $$72673 q - 106 q^{2} - 106 q^{3} - 106 q^{4} - 2 q^{5} - 170 q^{6} - 122 q^{7} - 106 q^{8} - 232 q^{9} - 128 q^{10} - 198 q^{11} - 188 q^{12} - 8 q^{13} - 58 q^{14} - 112 q^{15} - 106 q^{16} - 214 q^{17} + 6 q^{18} - 57 q^{19} - 88 q^{20} + 12 q^{21} - 78 q^{22} - 230 q^{23} + 6 q^{24} - 266 q^{25} - 266 q^{26} - 73 q^{27} - 122 q^{28} - 34 q^{29} - 120 q^{30} - 148 q^{31} - 176 q^{32} - 221 q^{33} - 324 q^{34} - 104 q^{35} - 218 q^{36} + 34 q^{37} - 136 q^{38} + 82 q^{39} - 208 q^{40} - 278 q^{41} - 76 q^{42} + 110 q^{43} - 72 q^{44} + 158 q^{45} - 196 q^{46} + 116 q^{47} - 12 q^{48} - 32 q^{49} - 88 q^{50} - 91 q^{51} + 40 q^{52} + 94 q^{53} + 86 q^{54} - 72 q^{55} - 116 q^{56} + 19 q^{57} + 96 q^{58} + 35 q^{59} - 40 q^{60} - 68 q^{61} + 134 q^{62} - 52 q^{63} + 38 q^{64} - 202 q^{65} - 142 q^{66} - 340 q^{67} - 10 q^{68} - 8 q^{69} - 120 q^{70} - 254 q^{71} - 308 q^{72} - 66 q^{73} - 220 q^{74} - 272 q^{75} - 506 q^{76} - 42 q^{77} - 596 q^{78} - 330 q^{79} - 168 q^{80} - 239 q^{81} - 494 q^{82} - 355 q^{83} - 658 q^{84} - 146 q^{85} - 406 q^{86} - 412 q^{87} - 510 q^{88} - 384 q^{89} - 728 q^{90} - 252 q^{91} - 634 q^{92} + 30 q^{93} - 722 q^{94} - 304 q^{95} - 416 q^{96} - 101 q^{97} - 712 q^{98} + 132 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2200))$$

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
2200.2.a $$\chi_{2200}(1, \cdot)$$ 2200.2.a.a 1 1
2200.2.a.b 1
2200.2.a.c 1
2200.2.a.d 1
2200.2.a.e 1
2200.2.a.f 1
2200.2.a.g 1
2200.2.a.h 1
2200.2.a.i 1
2200.2.a.j 1
2200.2.a.k 1
2200.2.a.l 2
2200.2.a.m 2
2200.2.a.n 2
2200.2.a.o 2
2200.2.a.p 2
2200.2.a.q 2
2200.2.a.r 2
2200.2.a.s 2
2200.2.a.t 3
2200.2.a.u 3
2200.2.a.v 3
2200.2.a.w 3
2200.2.a.x 4
2200.2.a.y 4
2200.2.b $$\chi_{2200}(1849, \cdot)$$ 2200.2.b.a 2 1
2200.2.b.b 2
2200.2.b.c 2
2200.2.b.d 2
2200.2.b.e 2
2200.2.b.f 4
2200.2.b.g 4
2200.2.b.h 4
2200.2.b.i 4
2200.2.b.j 4
2200.2.b.k 4
2200.2.b.l 6
2200.2.b.m 6
2200.2.c $$\chi_{2200}(1099, \cdot)$$ n/a 212 1
2200.2.f $$\chi_{2200}(351, \cdot)$$ None 0 1
2200.2.g $$\chi_{2200}(1101, \cdot)$$ n/a 190 1
2200.2.l $$\chi_{2200}(749, \cdot)$$ n/a 180 1
2200.2.m $$\chi_{2200}(2199, \cdot)$$ None 0 1
2200.2.p $$\chi_{2200}(1451, \cdot)$$ n/a 222 1
2200.2.r $$\chi_{2200}(243, \cdot)$$ n/a 360 2
2200.2.t $$\chi_{2200}(1693, \cdot)$$ n/a 424 2
2200.2.v $$\chi_{2200}(593, \cdot)$$ n/a 108 2
2200.2.x $$\chi_{2200}(1343, \cdot)$$ None 0 2
2200.2.y $$\chi_{2200}(361, \cdot)$$ n/a 360 4
2200.2.z $$\chi_{2200}(201, \cdot)$$ n/a 228 4
2200.2.ba $$\chi_{2200}(641, \cdot)$$ n/a 360 4
2200.2.bb $$\chi_{2200}(81, \cdot)$$ n/a 360 4
2200.2.bc $$\chi_{2200}(441, \cdot)$$ n/a 304 4
2200.2.bd $$\chi_{2200}(1281, \cdot)$$ n/a 360 4
2200.2.be $$\chi_{2200}(181, \cdot)$$ n/a 1424 4
2200.2.bf $$\chi_{2200}(831, \cdot)$$ None 0 4
2200.2.bi $$\chi_{2200}(1179, \cdot)$$ n/a 1424 4
2200.2.bj $$\chi_{2200}(289, \cdot)$$ n/a 360 4
2200.2.bm $$\chi_{2200}(439, \cdot)$$ None 0 4
2200.2.bn $$\chi_{2200}(309, \cdot)$$ n/a 1200 4
2200.2.bq $$\chi_{2200}(371, \cdot)$$ n/a 1424 4
2200.2.br $$\chi_{2200}(171, \cdot)$$ n/a 1424 4
2200.2.bs $$\chi_{2200}(211, \cdot)$$ n/a 1424 4
2200.2.bt $$\chi_{2200}(51, \cdot)$$ n/a 888 4
2200.2.cc $$\chi_{2200}(1109, \cdot)$$ n/a 1424 4
2200.2.cd $$\chi_{2200}(799, \cdot)$$ None 0 4
2200.2.ce $$\chi_{2200}(1119, \cdot)$$ None 0 4
2200.2.cf $$\chi_{2200}(479, \cdot)$$ None 0 4
2200.2.cg $$\chi_{2200}(389, \cdot)$$ n/a 1424 4
2200.2.ch $$\chi_{2200}(949, \cdot)$$ n/a 848 4
2200.2.ci $$\chi_{2200}(69, \cdot)$$ n/a 1424 4
2200.2.cj $$\chi_{2200}(39, \cdot)$$ None 0 4
2200.2.cs $$\chi_{2200}(131, \cdot)$$ n/a 1424 4
2200.2.cx $$\chi_{2200}(219, \cdot)$$ n/a 1424 4
2200.2.cy $$\chi_{2200}(89, \cdot)$$ n/a 296 4
2200.2.dh $$\chi_{2200}(1471, \cdot)$$ None 0 4
2200.2.di $$\chi_{2200}(581, \cdot)$$ n/a 1424 4
2200.2.dj $$\chi_{2200}(301, \cdot)$$ n/a 888 4
2200.2.dk $$\chi_{2200}(1461, \cdot)$$ n/a 1424 4
2200.2.dl $$\chi_{2200}(151, \cdot)$$ None 0 4
2200.2.dm $$\chi_{2200}(271, \cdot)$$ None 0 4
2200.2.dn $$\chi_{2200}(431, \cdot)$$ None 0 4
2200.2.do $$\chi_{2200}(141, \cdot)$$ n/a 1424 4
2200.2.dx $$\chi_{2200}(9, \cdot)$$ n/a 360 4
2200.2.dy $$\chi_{2200}(139, \cdot)$$ n/a 1424 4
2200.2.dz $$\chi_{2200}(19, \cdot)$$ n/a 1424 4
2200.2.ea $$\chi_{2200}(299, \cdot)$$ n/a 848 4
2200.2.eb $$\chi_{2200}(889, \cdot)$$ n/a 360 4
2200.2.ec $$\chi_{2200}(49, \cdot)$$ n/a 216 4
2200.2.ed $$\chi_{2200}(929, \cdot)$$ n/a 360 4
2200.2.ee $$\chi_{2200}(1019, \cdot)$$ n/a 1424 4
2200.2.eh $$\chi_{2200}(221, \cdot)$$ n/a 1200 4
2200.2.ei $$\chi_{2200}(791, \cdot)$$ None 0 4
2200.2.el $$\chi_{2200}(491, \cdot)$$ n/a 1424 4
2200.2.eo $$\chi_{2200}(79, \cdot)$$ None 0 4
2200.2.ep $$\chi_{2200}(229, \cdot)$$ n/a 1424 4
2200.2.er $$\chi_{2200}(223, \cdot)$$ None 0 8
2200.2.et $$\chi_{2200}(17, \cdot)$$ n/a 720 8
2200.2.ev $$\chi_{2200}(173, \cdot)$$ n/a 2848 8
2200.2.ex $$\chi_{2200}(467, \cdot)$$ n/a 2848 8
2200.2.ey $$\chi_{2200}(437, \cdot)$$ n/a 2848 8
2200.2.fa $$\chi_{2200}(203, \cdot)$$ n/a 2848 8
2200.2.fc $$\chi_{2200}(57, \cdot)$$ n/a 432 8
2200.2.fe $$\chi_{2200}(103, \cdot)$$ None 0 8
2200.2.fg $$\chi_{2200}(23, \cdot)$$ None 0 8
2200.2.fh $$\chi_{2200}(47, \cdot)$$ None 0 8
2200.2.fk $$\chi_{2200}(153, \cdot)$$ n/a 720 8
2200.2.fl $$\chi_{2200}(937, \cdot)$$ n/a 720 8
2200.2.fo $$\chi_{2200}(217, \cdot)$$ n/a 720 8
2200.2.fq $$\chi_{2200}(207, \cdot)$$ None 0 8
2200.2.fs $$\chi_{2200}(443, \cdot)$$ n/a 1696 8
2200.2.fu $$\chi_{2200}(197, \cdot)$$ n/a 2848 8
2200.2.fv $$\chi_{2200}(13, \cdot)$$ n/a 2848 8
2200.2.fy $$\chi_{2200}(237, \cdot)$$ n/a 2848 8
2200.2.ga $$\chi_{2200}(147, \cdot)$$ n/a 2848 8
2200.2.gc $$\chi_{2200}(67, \cdot)$$ n/a 2400 8
2200.2.gd $$\chi_{2200}(3, \cdot)$$ n/a 2848 8
2200.2.gg $$\chi_{2200}(293, \cdot)$$ n/a 1696 8
2200.2.gi $$\chi_{2200}(247, \cdot)$$ None 0 8
2200.2.gk $$\chi_{2200}(73, \cdot)$$ n/a 720 8

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2200))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2200)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(200))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(220))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(275))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(440))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(550))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1100))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2200))$$$$^{\oplus 1}$$