# Properties

 Label 1755.2 Level 1755 Weight 2 Dimension 76852 Nonzero newspaces 80 Sturm bound 435456 Trace bound 24

## Defining parameters

 Level: $$N$$ = $$1755 = 3^{3} \cdot 5 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$80$$ Sturm bound: $$435456$$ Trace bound: $$24$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1755))$$.

Total New Old
Modular forms 111744 78964 32780
Cusp forms 105985 76852 29133
Eisenstein series 5759 2112 3647

## Trace form

 $$76852 q - 88 q^{2} - 120 q^{3} - 144 q^{4} - 118 q^{5} - 336 q^{6} - 140 q^{7} - 24 q^{8} - 96 q^{9} + O(q^{10})$$ $$76852 q - 88 q^{2} - 120 q^{3} - 144 q^{4} - 118 q^{5} - 336 q^{6} - 140 q^{7} - 24 q^{8} - 96 q^{9} - 186 q^{10} - 196 q^{11} - 48 q^{12} - 134 q^{13} - 60 q^{14} - 150 q^{15} - 344 q^{16} - 4 q^{17} - 60 q^{18} - 136 q^{19} - 54 q^{20} - 384 q^{21} - 52 q^{22} - 72 q^{23} - 168 q^{24} - 178 q^{25} - 284 q^{26} - 276 q^{27} - 232 q^{28} + 16 q^{29} - 186 q^{30} - 308 q^{31} + 16 q^{32} - 120 q^{33} + 20 q^{34} - 100 q^{35} - 408 q^{36} - 40 q^{37} + 104 q^{38} - 114 q^{39} - 470 q^{40} - 212 q^{41} - 216 q^{42} - 140 q^{43} - 236 q^{44} - 306 q^{45} - 388 q^{46} - 220 q^{47} - 396 q^{48} - 112 q^{49} - 376 q^{50} - 504 q^{51} - 166 q^{52} - 352 q^{53} - 456 q^{54} - 456 q^{55} - 324 q^{56} - 180 q^{57} - 28 q^{58} - 40 q^{59} - 312 q^{60} - 252 q^{61} + 144 q^{62} - 60 q^{63} + 144 q^{64} + 15 q^{65} - 804 q^{66} + 40 q^{67} + 340 q^{68} - 60 q^{69} - 18 q^{70} + 220 q^{71} - 216 q^{72} + 92 q^{73} + 268 q^{74} - 174 q^{75} - 416 q^{76} + 12 q^{77} - 240 q^{78} - 428 q^{79} - 192 q^{80} - 384 q^{81} - 384 q^{82} - 12 q^{83} - 528 q^{84} - 282 q^{85} - 316 q^{86} - 300 q^{87} - 216 q^{88} - 324 q^{89} - 588 q^{90} - 446 q^{91} - 756 q^{92} - 540 q^{93} - 316 q^{94} - 426 q^{95} - 1344 q^{96} - 376 q^{97} - 1148 q^{98} - 660 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1755))$$

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
1755.2.a $$\chi_{1755}(1, \cdot)$$ 1755.2.a.a 1 1
1755.2.a.b 1
1755.2.a.c 1
1755.2.a.d 1
1755.2.a.e 1
1755.2.a.f 1
1755.2.a.g 2
1755.2.a.h 2
1755.2.a.i 2
1755.2.a.j 2
1755.2.a.k 2
1755.2.a.l 2
1755.2.a.m 4
1755.2.a.n 4
1755.2.a.o 4
1755.2.a.p 4
1755.2.a.q 4
1755.2.a.r 4
1755.2.a.s 4
1755.2.a.t 4
1755.2.a.u 7
1755.2.a.v 7
1755.2.b $$\chi_{1755}(1351, \cdot)$$ 1755.2.b.a 2 1
1755.2.b.b 2
1755.2.b.c 16
1755.2.b.d 18
1755.2.b.e 18
1755.2.b.f 20
1755.2.c $$\chi_{1755}(1054, \cdot)$$ 1755.2.c.a 16 1
1755.2.c.b 24
1755.2.c.c 24
1755.2.c.d 32
1755.2.h $$\chi_{1755}(649, \cdot)$$ n/a 112 1
1755.2.i $$\chi_{1755}(586, \cdot)$$ 1755.2.i.a 2 2
1755.2.i.b 2
1755.2.i.c 2
1755.2.i.d 2
1755.2.i.e 16
1755.2.i.f 16
1755.2.i.g 26
1755.2.i.h 30
1755.2.j $$\chi_{1755}(406, \cdot)$$ n/a 148 2
1755.2.k $$\chi_{1755}(451, \cdot)$$ n/a 112 2
1755.2.l $$\chi_{1755}(991, \cdot)$$ n/a 112 2
1755.2.n $$\chi_{1755}(892, \cdot)$$ n/a 224 2
1755.2.p $$\chi_{1755}(53, \cdot)$$ n/a 192 2
1755.2.q $$\chi_{1755}(944, \cdot)$$ n/a 224 2
1755.2.r $$\chi_{1755}(161, \cdot)$$ n/a 152 2
1755.2.v $$\chi_{1755}(1052, \cdot)$$ n/a 224 2
1755.2.w $$\chi_{1755}(1162, \cdot)$$ n/a 224 2
1755.2.ba $$\chi_{1755}(901, \cdot)$$ n/a 112 2
1755.2.bb $$\chi_{1755}(289, \cdot)$$ n/a 160 2
1755.2.be $$\chi_{1755}(64, \cdot)$$ n/a 160 2
1755.2.bf $$\chi_{1755}(244, \cdot)$$ n/a 224 2
1755.2.bk $$\chi_{1755}(1369, \cdot)$$ n/a 160 2
1755.2.bl $$\chi_{1755}(874, \cdot)$$ n/a 160 2
1755.2.bm $$\chi_{1755}(316, \cdot)$$ n/a 112 2
1755.2.br $$\chi_{1755}(469, \cdot)$$ n/a 144 2
1755.2.bs $$\chi_{1755}(919, \cdot)$$ n/a 224 2
1755.2.bt $$\chi_{1755}(181, \cdot)$$ n/a 112 2
1755.2.bu $$\chi_{1755}(946, \cdot)$$ n/a 148 2
1755.2.bx $$\chi_{1755}(199, \cdot)$$ n/a 160 2
1755.2.ca $$\chi_{1755}(196, \cdot)$$ n/a 864 6
1755.2.cb $$\chi_{1755}(61, \cdot)$$ n/a 1008 6
1755.2.cc $$\chi_{1755}(16, \cdot)$$ n/a 1008 6
1755.2.cd $$\chi_{1755}(253, \cdot)$$ n/a 320 4
1755.2.cf $$\chi_{1755}(388, \cdot)$$ n/a 320 4
1755.2.ci $$\chi_{1755}(163, \cdot)$$ n/a 448 4
1755.2.cj $$\chi_{1755}(73, \cdot)$$ n/a 320 4
1755.2.cl $$\chi_{1755}(152, \cdot)$$ n/a 320 4
1755.2.cp $$\chi_{1755}(71, \cdot)$$ n/a 224 4
1755.2.cq $$\chi_{1755}(89, \cdot)$$ n/a 320 4
1755.2.cr $$\chi_{1755}(17, \cdot)$$ n/a 320 4
1755.2.cu $$\chi_{1755}(602, \cdot)$$ n/a 320 4
1755.2.cv $$\chi_{1755}(233, \cdot)$$ n/a 320 4
1755.2.cy $$\chi_{1755}(647, \cdot)$$ n/a 448 4
1755.2.cz $$\chi_{1755}(431, \cdot)$$ n/a 296 4
1755.2.da $$\chi_{1755}(539, \cdot)$$ n/a 448 4
1755.2.df $$\chi_{1755}(44, \cdot)$$ n/a 320 4
1755.2.dg $$\chi_{1755}(206, \cdot)$$ n/a 224 4
1755.2.dh $$\chi_{1755}(314, \cdot)$$ n/a 320 4
1755.2.di $$\chi_{1755}(476, \cdot)$$ n/a 224 4
1755.2.dm $$\chi_{1755}(287, \cdot)$$ n/a 288 4
1755.2.dn $$\chi_{1755}(692, \cdot)$$ n/a 320 4
1755.2.dq $$\chi_{1755}(107, \cdot)$$ n/a 448 4
1755.2.ds $$\chi_{1755}(28, \cdot)$$ n/a 448 4
1755.2.dt $$\chi_{1755}(307, \cdot)$$ n/a 320 4
1755.2.dw $$\chi_{1755}(37, \cdot)$$ n/a 320 4
1755.2.dy $$\chi_{1755}(262, \cdot)$$ n/a 320 4
1755.2.dz $$\chi_{1755}(4, \cdot)$$ n/a 1488 6
1755.2.ed $$\chi_{1755}(49, \cdot)$$ n/a 1488 6
1755.2.eg $$\chi_{1755}(259, \cdot)$$ n/a 1488 6
1755.2.ej $$\chi_{1755}(139, \cdot)$$ n/a 1488 6
1755.2.el $$\chi_{1755}(166, \cdot)$$ n/a 1008 6
1755.2.em $$\chi_{1755}(376, \cdot)$$ n/a 1008 6
1755.2.eo $$\chi_{1755}(79, \cdot)$$ n/a 1296 6
1755.2.er $$\chi_{1755}(94, \cdot)$$ n/a 1488 6
1755.2.et $$\chi_{1755}(121, \cdot)$$ n/a 1008 6
1755.2.eu $$\chi_{1755}(187, \cdot)$$ n/a 2976 12
1755.2.ex $$\chi_{1755}(67, \cdot)$$ n/a 2976 12
1755.2.ey $$\chi_{1755}(292, \cdot)$$ n/a 2976 12
1755.2.fa $$\chi_{1755}(59, \cdot)$$ n/a 2976 12
1755.2.fc $$\chi_{1755}(86, \cdot)$$ n/a 2016 12
1755.2.fe $$\chi_{1755}(41, \cdot)$$ n/a 2016 12
1755.2.fg $$\chi_{1755}(68, \cdot)$$ n/a 2976 12
1755.2.fk $$\chi_{1755}(38, \cdot)$$ n/a 2976 12
1755.2.fl $$\chi_{1755}(212, \cdot)$$ n/a 2976 12
1755.2.fm $$\chi_{1755}(113, \cdot)$$ n/a 2976 12
1755.2.fn $$\chi_{1755}(92, \cdot)$$ n/a 2592 12
1755.2.fr $$\chi_{1755}(23, \cdot)$$ n/a 2976 12
1755.2.ft $$\chi_{1755}(254, \cdot)$$ n/a 2976 12
1755.2.fv $$\chi_{1755}(164, \cdot)$$ n/a 2976 12
1755.2.fx $$\chi_{1755}(11, \cdot)$$ n/a 2016 12
1755.2.fz $$\chi_{1755}(58, \cdot)$$ n/a 2976 12
1755.2.ga $$\chi_{1755}(7, \cdot)$$ n/a 2976 12
1755.2.gd $$\chi_{1755}(112, \cdot)$$ n/a 2976 12

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1755))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1755)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(135))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(351))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(585))$$$$^{\oplus 2}$$