# Properties

 Label 2310.2 Level 2310 Weight 2 Dimension 29863 Nonzero newspaces 48 Sturm bound 552960 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$552960$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2310))$$.

Total New Old
Modular forms 142080 29863 112217
Cusp forms 134401 29863 104538
Eisenstein series 7679 0 7679

## Trace form

 $$29863q - q^{2} - 17q^{3} - 17q^{4} - 41q^{5} - 53q^{6} - 105q^{7} - q^{8} - 113q^{9} + O(q^{10})$$ $$29863q - q^{2} - 17q^{3} - 17q^{4} - 41q^{5} - 53q^{6} - 105q^{7} - q^{8} - 113q^{9} - 49q^{10} - 97q^{11} - 25q^{12} - 94q^{13} - 9q^{14} - 21q^{15} - q^{16} - 130q^{17} + 59q^{18} - 140q^{19} + 15q^{20} + 15q^{21} + 15q^{22} - 56q^{23} + 35q^{24} - 65q^{25} + 34q^{26} + 247q^{27} + 47q^{28} + 82q^{29} + 123q^{30} - 16q^{31} - q^{32} + 267q^{33} + 142q^{34} + 203q^{35} + 83q^{36} + 282q^{37} + 124q^{38} + 266q^{39} + 23q^{40} + 38q^{41} + 115q^{42} + 164q^{43} + 95q^{44} + 103q^{45} + 232q^{46} + 256q^{47} + 15q^{48} + 111q^{49} + 175q^{50} + 178q^{51} + 242q^{52} + 234q^{53} + 103q^{54} + 483q^{55} - 33q^{56} + 264q^{57} + 402q^{58} + 340q^{59} + 119q^{60} + 674q^{61} + 288q^{62} + 531q^{63} - 17q^{64} + 706q^{65} + 447q^{66} + 972q^{67} + 270q^{68} + 776q^{69} + 359q^{70} + 856q^{71} + 79q^{72} + 726q^{73} + 298q^{74} + 563q^{75} + 204q^{76} + 583q^{77} + 258q^{78} + 656q^{79} + 39q^{80} + 703q^{81} + 238q^{82} + 492q^{83} + 151q^{84} + 246q^{85} + 420q^{86} + 410q^{87} + 151q^{88} + 278q^{89} + 91q^{90} + 674q^{91} - 24q^{92} + 192q^{93} + 192q^{94} + 180q^{95} - q^{96} + 310q^{97} - q^{98} + 343q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2310))$$

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
2310.2.a $$\chi_{2310}(1, \cdot)$$ 2310.2.a.a 1 1
2310.2.a.b 1
2310.2.a.c 1
2310.2.a.d 1
2310.2.a.e 1
2310.2.a.f 1
2310.2.a.g 1
2310.2.a.h 1
2310.2.a.i 1
2310.2.a.j 1
2310.2.a.k 1
2310.2.a.l 1
2310.2.a.m 1
2310.2.a.n 1
2310.2.a.o 1
2310.2.a.p 1
2310.2.a.q 1
2310.2.a.r 1
2310.2.a.s 1
2310.2.a.t 1
2310.2.a.u 1
2310.2.a.v 1
2310.2.a.w 2
2310.2.a.x 2
2310.2.a.y 2
2310.2.a.z 2
2310.2.a.ba 2
2310.2.a.bb 2
2310.2.a.bc 2
2310.2.a.bd 3
2310.2.d $$\chi_{2310}(769, \cdot)$$ 2310.2.d.a 24 1
2310.2.d.b 24
2310.2.d.c 24
2310.2.d.d 24
2310.2.e $$\chi_{2310}(1849, \cdot)$$ 2310.2.e.a 2 1
2310.2.e.b 2
2310.2.e.c 2
2310.2.e.d 2
2310.2.e.e 2
2310.2.e.f 2
2310.2.e.g 2
2310.2.e.h 4
2310.2.e.i 6
2310.2.e.j 6
2310.2.e.k 6
2310.2.e.l 6
2310.2.e.m 6
2310.2.e.n 8
2310.2.e.o 8
2310.2.f $$\chi_{2310}(881, \cdot)$$ n/a 112 1
2310.2.g $$\chi_{2310}(1121, \cdot)$$ 2310.2.g.a 4 1
2310.2.g.b 4
2310.2.g.c 8
2310.2.g.d 8
2310.2.g.e 12
2310.2.g.f 12
2310.2.g.g 24
2310.2.g.h 24
2310.2.j $$\chi_{2310}(419, \cdot)$$ n/a 160 1
2310.2.k $$\chi_{2310}(659, \cdot)$$ n/a 144 1
2310.2.p $$\chi_{2310}(1231, \cdot)$$ 2310.2.p.a 4 1
2310.2.p.b 4
2310.2.p.c 12
2310.2.p.d 12
2310.2.p.e 16
2310.2.p.f 16
2310.2.q $$\chi_{2310}(331, \cdot)$$ n/a 112 2
2310.2.r $$\chi_{2310}(923, \cdot)$$ n/a 384 2
2310.2.u $$\chi_{2310}(617, \cdot)$$ n/a 240 2
2310.2.v $$\chi_{2310}(727, \cdot)$$ n/a 160 2
2310.2.y $$\chi_{2310}(43, \cdot)$$ n/a 144 2
2310.2.z $$\chi_{2310}(421, \cdot)$$ n/a 192 4
2310.2.bc $$\chi_{2310}(551, \cdot)$$ n/a 208 2
2310.2.bd $$\chi_{2310}(1451, \cdot)$$ n/a 256 2
2310.2.be $$\chi_{2310}(439, \cdot)$$ n/a 192 2
2310.2.bf $$\chi_{2310}(529, \cdot)$$ n/a 160 2
2310.2.bi $$\chi_{2310}(241, \cdot)$$ n/a 128 2
2310.2.bn $$\chi_{2310}(89, \cdot)$$ n/a 320 2
2310.2.bo $$\chi_{2310}(989, \cdot)$$ n/a 384 2
2310.2.bp $$\chi_{2310}(391, \cdot)$$ n/a 256 4
2310.2.bu $$\chi_{2310}(29, \cdot)$$ n/a 576 4
2310.2.bv $$\chi_{2310}(839, \cdot)$$ n/a 768 4
2310.2.by $$\chi_{2310}(281, \cdot)$$ n/a 384 4
2310.2.bz $$\chi_{2310}(251, \cdot)$$ n/a 512 4
2310.2.ca $$\chi_{2310}(169, \cdot)$$ n/a 288 4
2310.2.cb $$\chi_{2310}(139, \cdot)$$ n/a 384 4
2310.2.cf $$\chi_{2310}(397, \cdot)$$ n/a 320 4
2310.2.cg $$\chi_{2310}(373, \cdot)$$ n/a 384 4
2310.2.cj $$\chi_{2310}(593, \cdot)$$ n/a 768 4
2310.2.ck $$\chi_{2310}(23, \cdot)$$ n/a 640 4
2310.2.cm $$\chi_{2310}(361, \cdot)$$ n/a 512 8
2310.2.cn $$\chi_{2310}(127, \cdot)$$ n/a 576 8
2310.2.cq $$\chi_{2310}(97, \cdot)$$ n/a 768 8
2310.2.cr $$\chi_{2310}(113, \cdot)$$ n/a 1152 8
2310.2.cu $$\chi_{2310}(83, \cdot)$$ n/a 1536 8
2310.2.cv $$\chi_{2310}(149, \cdot)$$ n/a 1536 8
2310.2.cw $$\chi_{2310}(59, \cdot)$$ n/a 1536 8
2310.2.db $$\chi_{2310}(61, \cdot)$$ n/a 512 8
2310.2.de $$\chi_{2310}(289, \cdot)$$ n/a 768 8
2310.2.df $$\chi_{2310}(19, \cdot)$$ n/a 768 8
2310.2.dg $$\chi_{2310}(431, \cdot)$$ n/a 1024 8
2310.2.dh $$\chi_{2310}(311, \cdot)$$ n/a 1024 8
2310.2.dl $$\chi_{2310}(53, \cdot)$$ n/a 3072 16
2310.2.dm $$\chi_{2310}(17, \cdot)$$ n/a 3072 16
2310.2.dp $$\chi_{2310}(193, \cdot)$$ n/a 1536 16
2310.2.dq $$\chi_{2310}(103, \cdot)$$ n/a 1536 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2310))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2310)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(210))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(231))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(330))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(385))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(462))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(770))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1155))$$$$^{\oplus 2}$$