# Properties

 Label 2805.2 Level 2805 Weight 2 Dimension 183985 Nonzero newspaces 72 Sturm bound 1105920 Trace bound 14

## Defining parameters

 Level: $$N$$ = $$2805 = 3 \cdot 5 \cdot 11 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$72$$ Sturm bound: $$1105920$$ Trace bound: $$14$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2805))$$.

Total New Old
Modular forms 281600 187233 94367
Cusp forms 271361 183985 87376
Eisenstein series 10239 3248 6991

## Trace form

 $$183985q - 13q^{2} - 115q^{3} - 241q^{4} + q^{5} - 309q^{6} - 200q^{7} + 47q^{8} - 67q^{9} + O(q^{10})$$ $$183985q - 13q^{2} - 115q^{3} - 241q^{4} + q^{5} - 309q^{6} - 200q^{7} + 47q^{8} - 67q^{9} - 261q^{10} + 41q^{11} - 89q^{12} - 162q^{13} + 176q^{14} - 81q^{15} - 217q^{16} + 93q^{17} - 61q^{18} - 76q^{19} + 187q^{20} - 152q^{21} - 5q^{22} + 72q^{23} + 95q^{24} - 131q^{25} + 370q^{26} - 175q^{27} + 200q^{28} + 142q^{29} - 29q^{30} - 408q^{31} + 191q^{32} - 99q^{33} - 53q^{34} + 184q^{35} - 201q^{36} + 46q^{37} + 324q^{38} + 22q^{39} - 201q^{40} + 314q^{41} - 120q^{42} - 20q^{43} + 95q^{44} - 329q^{45} - 536q^{46} - 72q^{47} - 441q^{48} - 375q^{49} - 113q^{50} - 491q^{51} - 878q^{52} - 66q^{53} - 237q^{54} - 499q^{55} - 200q^{56} - 300q^{57} - 310q^{58} - 60q^{59} - 369q^{60} - 578q^{61} + 80q^{62} + 16q^{63} - 681q^{64} + 70q^{65} - 469q^{66} - 372q^{67} + 399q^{68} - 28q^{69} - 224q^{70} + 120q^{71} + 31q^{72} + 122q^{73} + 154q^{74} - 29q^{75} - 388q^{76} + 240q^{77} - 22q^{78} + 64q^{79} - 413q^{80} - 59q^{81} - 418q^{82} + 380q^{83} - 592q^{84} - 783q^{85} - 108q^{86} - 314q^{87} - 361q^{88} - 166q^{89} - 613q^{90} - 1088q^{91} - 864q^{92} - 508q^{93} - 1152q^{94} - 448q^{95} - 1465q^{96} - 758q^{97} - 773q^{98} - 579q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2805))$$

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
2805.2.a $$\chi_{2805}(1, \cdot)$$ 2805.2.a.a 1 1
2805.2.a.b 1
2805.2.a.c 1
2805.2.a.d 1
2805.2.a.e 1
2805.2.a.f 2
2805.2.a.g 4
2805.2.a.h 4
2805.2.a.i 4
2805.2.a.j 4
2805.2.a.k 5
2805.2.a.l 5
2805.2.a.m 6
2805.2.a.n 6
2805.2.a.o 7
2805.2.a.p 7
2805.2.a.q 7
2805.2.a.r 7
2805.2.a.s 7
2805.2.a.t 8
2805.2.a.u 8
2805.2.a.v 9
2805.2.c $$\chi_{2805}(1684, \cdot)$$ n/a 160 1
2805.2.d $$\chi_{2805}(2804, \cdot)$$ n/a 424 1
2805.2.g $$\chi_{2805}(1189, \cdot)$$ n/a 184 1
2805.2.h $$\chi_{2805}(494, \cdot)$$ n/a 384 1
2805.2.j $$\chi_{2805}(1616, \cdot)$$ n/a 256 1
2805.2.m $$\chi_{2805}(2311, \cdot)$$ n/a 120 1
2805.2.n $$\chi_{2805}(1121, \cdot)$$ n/a 288 1
2805.2.r $$\chi_{2805}(956, \cdot)$$ n/a 576 2
2805.2.s $$\chi_{2805}(166, \cdot)$$ n/a 240 2
2805.2.u $$\chi_{2805}(208, \cdot)$$ n/a 432 2
2805.2.w $$\chi_{2805}(353, \cdot)$$ n/a 720 2
2805.2.y $$\chi_{2805}(1937, \cdot)$$ n/a 720 2
2805.2.bb $$\chi_{2805}(307, \cdot)$$ n/a 384 2
2805.2.bc $$\chi_{2805}(188, \cdot)$$ n/a 640 2
2805.2.bf $$\chi_{2805}(373, \cdot)$$ n/a 432 2
2805.2.bh $$\chi_{2805}(1033, \cdot)$$ n/a 432 2
2805.2.bj $$\chi_{2805}(2333, \cdot)$$ n/a 720 2
2805.2.bk $$\chi_{2805}(1024, \cdot)$$ n/a 368 2
2805.2.bn $$\chi_{2805}(659, \cdot)$$ n/a 848 2
2805.2.bo $$\chi_{2805}(256, \cdot)$$ n/a 512 4
2805.2.bp $$\chi_{2805}(637, \cdot)$$ n/a 864 4
2805.2.bs $$\chi_{2805}(848, \cdot)$$ n/a 1440 4
2805.2.bt $$\chi_{2805}(824, \cdot)$$ n/a 1696 4
2805.2.bu $$\chi_{2805}(331, \cdot)$$ n/a 480 4
2805.2.bz $$\chi_{2805}(529, \cdot)$$ n/a 704 4
2805.2.ca $$\chi_{2805}(461, \cdot)$$ n/a 1152 4
2805.2.cb $$\chi_{2805}(287, \cdot)$$ n/a 1440 4
2805.2.ce $$\chi_{2805}(43, \cdot)$$ n/a 864 4
2805.2.ch $$\chi_{2805}(101, \cdot)$$ n/a 1152 4
2805.2.ci $$\chi_{2805}(16, \cdot)$$ n/a 576 4
2805.2.cl $$\chi_{2805}(596, \cdot)$$ n/a 1024 4
2805.2.cn $$\chi_{2805}(239, \cdot)$$ n/a 1536 4
2805.2.co $$\chi_{2805}(169, \cdot)$$ n/a 864 4
2805.2.cr $$\chi_{2805}(1019, \cdot)$$ n/a 1696 4
2805.2.cs $$\chi_{2805}(664, \cdot)$$ n/a 768 4
2805.2.cw $$\chi_{2805}(362, \cdot)$$ n/a 3392 8
2805.2.cx $$\chi_{2805}(133, \cdot)$$ n/a 1440 8
2805.2.cz $$\chi_{2805}(241, \cdot)$$ n/a 1152 8
2805.2.da $$\chi_{2805}(419, \cdot)$$ n/a 2880 8
2805.2.dc $$\chi_{2805}(56, \cdot)$$ n/a 1920 8
2805.2.df $$\chi_{2805}(109, \cdot)$$ n/a 1728 8
2805.2.dg $$\chi_{2805}(197, \cdot)$$ n/a 3392 8
2805.2.dh $$\chi_{2805}(793, \cdot)$$ n/a 1440 8
2805.2.dk $$\chi_{2805}(149, \cdot)$$ n/a 3392 8
2805.2.dn $$\chi_{2805}(4, \cdot)$$ n/a 1728 8
2805.2.dp $$\chi_{2805}(38, \cdot)$$ n/a 3392 8
2805.2.dr $$\chi_{2805}(13, \cdot)$$ n/a 1728 8
2805.2.ds $$\chi_{2805}(118, \cdot)$$ n/a 1728 8
2805.2.dv $$\chi_{2805}(137, \cdot)$$ n/a 3072 8
2805.2.dw $$\chi_{2805}(52, \cdot)$$ n/a 1536 8
2805.2.dz $$\chi_{2805}(152, \cdot)$$ n/a 3392 8
2805.2.ea $$\chi_{2805}(608, \cdot)$$ n/a 3392 8
2805.2.ec $$\chi_{2805}(217, \cdot)$$ n/a 1728 8
2805.2.ef $$\chi_{2805}(361, \cdot)$$ n/a 1152 8
2805.2.eg $$\chi_{2805}(446, \cdot)$$ n/a 2304 8
2805.2.ej $$\chi_{2805}(257, \cdot)$$ n/a 6784 16
2805.2.ek $$\chi_{2805}(172, \cdot)$$ n/a 3456 16
2805.2.em $$\chi_{2805}(49, \cdot)$$ n/a 3456 16
2805.2.en $$\chi_{2805}(161, \cdot)$$ n/a 4608 16
2805.2.es $$\chi_{2805}(134, \cdot)$$ n/a 6784 16
2805.2.et $$\chi_{2805}(196, \cdot)$$ n/a 2304 16
2805.2.ev $$\chi_{2805}(127, \cdot)$$ n/a 3456 16
2805.2.ew $$\chi_{2805}(53, \cdot)$$ n/a 6784 16
2805.2.fa $$\chi_{2805}(37, \cdot)$$ n/a 6912 32
2805.2.fb $$\chi_{2805}(62, \cdot)$$ n/a 13568 32
2805.2.fd $$\chi_{2805}(71, \cdot)$$ n/a 9216 32
2805.2.fe $$\chi_{2805}(79, \cdot)$$ n/a 6912 32
2805.2.fg $$\chi_{2805}(46, \cdot)$$ n/a 4608 32
2805.2.fj $$\chi_{2805}(14, \cdot)$$ n/a 13568 32
2805.2.fk $$\chi_{2805}(148, \cdot)$$ n/a 6912 32
2805.2.fl $$\chi_{2805}(107, \cdot)$$ n/a 13568 32

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2805))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2805)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(85))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(187))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(255))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(561))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(935))$$$$^{\oplus 2}$$