# Properties

 Label 2320.2 Level 2320 Weight 2 Dimension 82232 Nonzero newspaces 52 Sturm bound 645120 Trace bound 13

## Defining parameters

 Level: $$N$$ = $$2320 = 2^{4} \cdot 5 \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$52$$ Sturm bound: $$645120$$ Trace bound: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2320))$$.

Total New Old
Modular forms 164416 83692 80724
Cusp forms 158145 82232 75913
Eisenstein series 6271 1460 4811

## Trace form

 $$82232 q - 104 q^{2} - 80 q^{3} - 96 q^{4} - 194 q^{5} - 288 q^{6} - 72 q^{7} - 80 q^{8} - 20 q^{9} + O(q^{10})$$ $$82232 q - 104 q^{2} - 80 q^{3} - 96 q^{4} - 194 q^{5} - 288 q^{6} - 72 q^{7} - 80 q^{8} - 20 q^{9} - 152 q^{10} - 220 q^{11} - 112 q^{12} - 120 q^{13} - 112 q^{14} - 82 q^{15} - 336 q^{16} - 216 q^{17} - 88 q^{18} - 28 q^{19} - 144 q^{20} - 332 q^{21} - 96 q^{22} - 48 q^{23} - 96 q^{24} - 22 q^{25} - 288 q^{26} - 92 q^{27} - 128 q^{28} - 120 q^{29} - 392 q^{30} - 308 q^{31} - 144 q^{32} - 284 q^{33} - 208 q^{34} - 146 q^{35} - 448 q^{36} - 176 q^{37} - 256 q^{38} - 124 q^{39} - 328 q^{40} - 140 q^{41} - 256 q^{42} - 64 q^{43} - 224 q^{44} - 246 q^{45} - 384 q^{46} - 8 q^{47} - 192 q^{48} - 220 q^{49} - 264 q^{50} - 180 q^{51} - 176 q^{52} - 128 q^{53} - 192 q^{54} - 86 q^{55} - 336 q^{56} + 80 q^{57} - 128 q^{58} - 112 q^{59} - 88 q^{60} - 420 q^{61} - 32 q^{62} - 136 q^{63} - 48 q^{64} - 278 q^{65} - 160 q^{66} - 184 q^{67} + 16 q^{68} - 164 q^{69} + 8 q^{70} - 340 q^{71} + 160 q^{72} + 16 q^{73} + 80 q^{74} - 338 q^{75} - 128 q^{76} - 124 q^{77} + 160 q^{78} - 260 q^{79} + 24 q^{80} - 640 q^{81} + 32 q^{82} - 256 q^{83} + 176 q^{84} - 190 q^{85} - 176 q^{86} - 200 q^{87} + 20 q^{89} + 80 q^{90} - 276 q^{91} - 112 q^{92} - 28 q^{93} - 48 q^{94} - 230 q^{95} - 240 q^{96} - 64 q^{97} - 184 q^{98} + 108 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2320))$$

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
2320.2.a $$\chi_{2320}(1, \cdot)$$ 2320.2.a.a 1 1
2320.2.a.b 1
2320.2.a.c 1
2320.2.a.d 1
2320.2.a.e 1
2320.2.a.f 1
2320.2.a.g 1
2320.2.a.h 1
2320.2.a.i 2
2320.2.a.j 2
2320.2.a.k 2
2320.2.a.l 3
2320.2.a.m 3
2320.2.a.n 3
2320.2.a.o 3
2320.2.a.p 3
2320.2.a.q 3
2320.2.a.r 3
2320.2.a.s 3
2320.2.a.t 3
2320.2.a.u 5
2320.2.a.v 5
2320.2.a.w 5
2320.2.d $$\chi_{2320}(929, \cdot)$$ 2320.2.d.a 2 1
2320.2.d.b 2
2320.2.d.c 4
2320.2.d.d 4
2320.2.d.e 4
2320.2.d.f 4
2320.2.d.g 6
2320.2.d.h 10
2320.2.d.i 10
2320.2.d.j 16
2320.2.d.k 22
2320.2.e $$\chi_{2320}(1449, \cdot)$$ None 0 1
2320.2.f $$\chi_{2320}(1161, \cdot)$$ None 0 1
2320.2.g $$\chi_{2320}(1681, \cdot)$$ 2320.2.g.a 2 1
2320.2.g.b 2
2320.2.g.c 2
2320.2.g.d 4
2320.2.g.e 4
2320.2.g.f 4
2320.2.g.g 4
2320.2.g.h 4
2320.2.g.i 6
2320.2.g.j 14
2320.2.g.k 14
2320.2.j $$\chi_{2320}(289, \cdot)$$ 2320.2.j.a 4 1
2320.2.j.b 4
2320.2.j.c 4
2320.2.j.d 8
2320.2.j.e 8
2320.2.j.f 16
2320.2.j.g 22
2320.2.j.h 22
2320.2.k $$\chi_{2320}(2089, \cdot)$$ None 0 1
2320.2.p $$\chi_{2320}(521, \cdot)$$ None 0 1
2320.2.q $$\chi_{2320}(99, \cdot)$$ n/a 712 2
2320.2.t $$\chi_{2320}(347, \cdot)$$ n/a 712 2
2320.2.u $$\chi_{2320}(713, \cdot)$$ None 0 2
2320.2.w $$\chi_{2320}(17, \cdot)$$ n/a 176 2
2320.2.z $$\chi_{2320}(523, \cdot)$$ n/a 672 2
2320.2.bb $$\chi_{2320}(331, \cdot)$$ n/a 480 2
2320.2.bc $$\chi_{2320}(191, \cdot)$$ n/a 120 2
2320.2.bf $$\chi_{2320}(1101, \cdot)$$ n/a 480 2
2320.2.bh $$\chi_{2320}(581, \cdot)$$ n/a 448 2
2320.2.bi $$\chi_{2320}(1351, \cdot)$$ None 0 2
2320.2.bl $$\chi_{2320}(853, \cdot)$$ n/a 712 2
2320.2.bo $$\chi_{2320}(1103, \cdot)$$ n/a 168 2
2320.2.bp $$\chi_{2320}(1623, \cdot)$$ None 0 2
2320.2.bq $$\chi_{2320}(1293, \cdot)$$ n/a 712 2
2320.2.bs $$\chi_{2320}(133, \cdot)$$ n/a 712 2
2320.2.bu $$\chi_{2320}(407, \cdot)$$ None 0 2
2320.2.bv $$\chi_{2320}(463, \cdot)$$ n/a 180 2
2320.2.bz $$\chi_{2320}(597, \cdot)$$ n/a 712 2
2320.2.cb $$\chi_{2320}(679, \cdot)$$ None 0 2
2320.2.cc $$\chi_{2320}(349, \cdot)$$ n/a 672 2
2320.2.ce $$\chi_{2320}(869, \cdot)$$ n/a 712 2
2320.2.ch $$\chi_{2320}(1119, \cdot)$$ n/a 180 2
2320.2.cj $$\chi_{2320}(1259, \cdot)$$ n/a 712 2
2320.2.ck $$\chi_{2320}(987, \cdot)$$ n/a 672 2
2320.2.cn $$\chi_{2320}(737, \cdot)$$ n/a 176 2
2320.2.cp $$\chi_{2320}(1177, \cdot)$$ None 0 2
2320.2.cq $$\chi_{2320}(1507, \cdot)$$ n/a 712 2
2320.2.cs $$\chi_{2320}(1491, \cdot)$$ n/a 480 2
2320.2.cu $$\chi_{2320}(81, \cdot)$$ n/a 360 6
2320.2.cv $$\chi_{2320}(121, \cdot)$$ None 0 6
2320.2.da $$\chi_{2320}(169, \cdot)$$ None 0 6
2320.2.db $$\chi_{2320}(129, \cdot)$$ n/a 528 6
2320.2.de $$\chi_{2320}(241, \cdot)$$ n/a 360 6
2320.2.df $$\chi_{2320}(281, \cdot)$$ None 0 6
2320.2.dg $$\chi_{2320}(9, \cdot)$$ None 0 6
2320.2.dh $$\chi_{2320}(49, \cdot)$$ n/a 528 6
2320.2.dl $$\chi_{2320}(11, \cdot)$$ n/a 2880 12
2320.2.dn $$\chi_{2320}(67, \cdot)$$ n/a 4272 12
2320.2.do $$\chi_{2320}(97, \cdot)$$ n/a 1056 12
2320.2.dq $$\chi_{2320}(73, \cdot)$$ None 0 12
2320.2.dt $$\chi_{2320}(83, \cdot)$$ n/a 4272 12
2320.2.du $$\chi_{2320}(19, \cdot)$$ n/a 4272 12
2320.2.dw $$\chi_{2320}(79, \cdot)$$ n/a 1080 12
2320.2.dz $$\chi_{2320}(429, \cdot)$$ n/a 4272 12
2320.2.eb $$\chi_{2320}(109, \cdot)$$ n/a 4272 12
2320.2.ec $$\chi_{2320}(39, \cdot)$$ None 0 12
2320.2.ef $$\chi_{2320}(437, \cdot)$$ n/a 4272 12
2320.2.ei $$\chi_{2320}(63, \cdot)$$ n/a 1080 12
2320.2.ej $$\chi_{2320}(7, \cdot)$$ None 0 12
2320.2.ek $$\chi_{2320}(293, \cdot)$$ n/a 4272 12
2320.2.em $$\chi_{2320}(37, \cdot)$$ n/a 4272 12
2320.2.eo $$\chi_{2320}(167, \cdot)$$ None 0 12
2320.2.ep $$\chi_{2320}(223, \cdot)$$ n/a 1080 12
2320.2.et $$\chi_{2320}(77, \cdot)$$ n/a 4272 12
2320.2.ev $$\chi_{2320}(311, \cdot)$$ None 0 12
2320.2.ew $$\chi_{2320}(341, \cdot)$$ n/a 2880 12
2320.2.ey $$\chi_{2320}(141, \cdot)$$ n/a 2880 12
2320.2.fb $$\chi_{2320}(31, \cdot)$$ n/a 720 12
2320.2.fc $$\chi_{2320}(171, \cdot)$$ n/a 2880 12
2320.2.fe $$\chi_{2320}(123, \cdot)$$ n/a 4272 12
2320.2.fh $$\chi_{2320}(537, \cdot)$$ None 0 12
2320.2.fj $$\chi_{2320}(113, \cdot)$$ n/a 1056 12
2320.2.fk $$\chi_{2320}(187, \cdot)$$ n/a 4272 12
2320.2.fn $$\chi_{2320}(259, \cdot)$$ n/a 4272 12

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2320))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2320)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(58))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(116))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(145))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(232))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(290))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(464))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(580))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1160))$$$$^{\oplus 2}$$