# Properties

 Label 2320.4 Level 2320 Weight 4 Dimension 248156 Nonzero newspaces 52 Sturm bound 1290240 Trace bound 13

## Defining parameters

 Level: $$N$$ = $$2320 = 2^{4} \cdot 5 \cdot 29$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$52$$ Sturm bound: $$1290240$$ Trace bound: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(2320))$$.

Total New Old
Modular forms 486976 249616 237360
Cusp forms 480704 248156 232548
Eisenstein series 6272 1460 4812

## Trace form

 $$248156 q - 104 q^{2} - 64 q^{3} - 64 q^{4} - 198 q^{5} - 432 q^{6} - 168 q^{7} - 272 q^{8} - 64 q^{9} + O(q^{10})$$ $$248156 q - 104 q^{2} - 64 q^{3} - 64 q^{4} - 198 q^{5} - 432 q^{6} - 168 q^{7} - 272 q^{8} - 64 q^{9} - 288 q^{10} + 20 q^{11} + 304 q^{12} + 144 q^{13} + 656 q^{14} - 354 q^{15} + 816 q^{16} - 240 q^{17} + 600 q^{18} - 812 q^{19} - 544 q^{20} - 1100 q^{21} - 2448 q^{22} - 16 q^{23} - 3488 q^{24} - 354 q^{25} - 1360 q^{26} + 836 q^{27} - 420 q^{29} - 1112 q^{30} + 1356 q^{31} + 2416 q^{32} + 388 q^{33} + 2800 q^{34} + 1390 q^{35} + 768 q^{36} + 1832 q^{37} - 880 q^{38} + 1508 q^{39} + 3416 q^{40} + 1500 q^{41} + 2464 q^{42} - 2768 q^{43} + 5504 q^{44} + 1462 q^{45} + 3840 q^{46} - 4040 q^{47} + 2752 q^{48} - 536 q^{49} - 3880 q^{50} - 6292 q^{51} - 8528 q^{52} - 5704 q^{53} - 9056 q^{54} - 2662 q^{55} - 2256 q^{56} - 3984 q^{57} - 88 q^{58} + 5088 q^{59} + 488 q^{60} + 3636 q^{61} - 416 q^{62} + 1144 q^{63} + 9680 q^{64} - 4318 q^{65} + 11168 q^{66} - 2440 q^{67} + 2320 q^{68} + 3100 q^{69} + 1752 q^{70} + 1484 q^{71} - 1248 q^{72} + 4232 q^{73} - 10528 q^{74} + 13374 q^{75} - 13792 q^{76} - 540 q^{77} - 26720 q^{78} + 700 q^{79} - 18088 q^{80} + 5380 q^{81} - 14720 q^{82} + 6288 q^{83} - 10192 q^{84} + 6378 q^{85} + 10016 q^{86} + 6040 q^{87} + 4672 q^{88} + 3276 q^{89} + 11080 q^{90} - 84 q^{91} + 12496 q^{92} - 14812 q^{93} + 1584 q^{94} - 9750 q^{95} + 6672 q^{96} + 15512 q^{97} + 8296 q^{98} + 45948 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(2320))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
2320.4.a $$\chi_{2320}(1, \cdot)$$ 2320.4.a.a 1 1
2320.4.a.b 1
2320.4.a.c 1
2320.4.a.d 1
2320.4.a.e 1
2320.4.a.f 1
2320.4.a.g 3
2320.4.a.h 3
2320.4.a.i 3
2320.4.a.j 3
2320.4.a.k 5
2320.4.a.l 5
2320.4.a.m 5
2320.4.a.n 6
2320.4.a.o 6
2320.4.a.p 6
2320.4.a.q 6
2320.4.a.r 7
2320.4.a.s 7
2320.4.a.t 8
2320.4.a.u 8
2320.4.a.v 8
2320.4.a.w 9
2320.4.a.x 9
2320.4.a.y 9
2320.4.a.z 11
2320.4.a.ba 11
2320.4.a.bb 11
2320.4.a.bc 13
2320.4.d $$\chi_{2320}(929, \cdot)$$ n/a 252 1
2320.4.e $$\chi_{2320}(1449, \cdot)$$ None 0 1
2320.4.f $$\chi_{2320}(1161, \cdot)$$ None 0 1
2320.4.g $$\chi_{2320}(1681, \cdot)$$ n/a 180 1
2320.4.j $$\chi_{2320}(289, \cdot)$$ n/a 268 1
2320.4.k $$\chi_{2320}(2089, \cdot)$$ None 0 1
2320.4.p $$\chi_{2320}(521, \cdot)$$ None 0 1
2320.4.q $$\chi_{2320}(99, \cdot)$$ n/a 2152 2
2320.4.t $$\chi_{2320}(347, \cdot)$$ n/a 2152 2
2320.4.u $$\chi_{2320}(713, \cdot)$$ None 0 2
2320.4.w $$\chi_{2320}(17, \cdot)$$ n/a 536 2
2320.4.z $$\chi_{2320}(523, \cdot)$$ n/a 2016 2
2320.4.bb $$\chi_{2320}(331, \cdot)$$ n/a 1440 2
2320.4.bc $$\chi_{2320}(191, \cdot)$$ n/a 360 2
2320.4.bf $$\chi_{2320}(1101, \cdot)$$ n/a 1440 2
2320.4.bh $$\chi_{2320}(581, \cdot)$$ n/a 1344 2
2320.4.bi $$\chi_{2320}(1351, \cdot)$$ None 0 2
2320.4.bl $$\chi_{2320}(853, \cdot)$$ n/a 2152 2
2320.4.bo $$\chi_{2320}(1103, \cdot)$$ n/a 504 2
2320.4.bp $$\chi_{2320}(1623, \cdot)$$ None 0 2
2320.4.bq $$\chi_{2320}(1293, \cdot)$$ n/a 2152 2
2320.4.bs $$\chi_{2320}(133, \cdot)$$ n/a 2152 2
2320.4.bu $$\chi_{2320}(407, \cdot)$$ None 0 2
2320.4.bv $$\chi_{2320}(463, \cdot)$$ n/a 540 2
2320.4.bz $$\chi_{2320}(597, \cdot)$$ n/a 2152 2
2320.4.cb $$\chi_{2320}(679, \cdot)$$ None 0 2
2320.4.cc $$\chi_{2320}(349, \cdot)$$ n/a 2016 2
2320.4.ce $$\chi_{2320}(869, \cdot)$$ n/a 2152 2
2320.4.ch $$\chi_{2320}(1119, \cdot)$$ n/a 540 2
2320.4.cj $$\chi_{2320}(1259, \cdot)$$ n/a 2152 2
2320.4.ck $$\chi_{2320}(987, \cdot)$$ n/a 2016 2
2320.4.cn $$\chi_{2320}(737, \cdot)$$ n/a 536 2
2320.4.cp $$\chi_{2320}(1177, \cdot)$$ None 0 2
2320.4.cq $$\chi_{2320}(1507, \cdot)$$ n/a 2152 2
2320.4.cs $$\chi_{2320}(1491, \cdot)$$ n/a 1440 2
2320.4.cu $$\chi_{2320}(81, \cdot)$$ n/a 1080 6
2320.4.cv $$\chi_{2320}(121, \cdot)$$ None 0 6
2320.4.da $$\chi_{2320}(169, \cdot)$$ None 0 6
2320.4.db $$\chi_{2320}(129, \cdot)$$ n/a 1608 6
2320.4.de $$\chi_{2320}(241, \cdot)$$ n/a 1080 6
2320.4.df $$\chi_{2320}(281, \cdot)$$ None 0 6
2320.4.dg $$\chi_{2320}(9, \cdot)$$ None 0 6
2320.4.dh $$\chi_{2320}(49, \cdot)$$ n/a 1608 6
2320.4.dl $$\chi_{2320}(11, \cdot)$$ n/a 8640 12
2320.4.dn $$\chi_{2320}(67, \cdot)$$ n/a 12912 12
2320.4.do $$\chi_{2320}(97, \cdot)$$ n/a 3216 12
2320.4.dq $$\chi_{2320}(73, \cdot)$$ None 0 12
2320.4.dt $$\chi_{2320}(83, \cdot)$$ n/a 12912 12
2320.4.du $$\chi_{2320}(19, \cdot)$$ n/a 12912 12
2320.4.dw $$\chi_{2320}(79, \cdot)$$ n/a 3240 12
2320.4.dz $$\chi_{2320}(429, \cdot)$$ n/a 12912 12
2320.4.eb $$\chi_{2320}(109, \cdot)$$ n/a 12912 12
2320.4.ec $$\chi_{2320}(39, \cdot)$$ None 0 12
2320.4.ef $$\chi_{2320}(437, \cdot)$$ n/a 12912 12
2320.4.ei $$\chi_{2320}(63, \cdot)$$ n/a 3240 12
2320.4.ej $$\chi_{2320}(7, \cdot)$$ None 0 12
2320.4.ek $$\chi_{2320}(293, \cdot)$$ n/a 12912 12
2320.4.em $$\chi_{2320}(37, \cdot)$$ n/a 12912 12
2320.4.eo $$\chi_{2320}(167, \cdot)$$ None 0 12
2320.4.ep $$\chi_{2320}(223, \cdot)$$ n/a 3240 12
2320.4.et $$\chi_{2320}(77, \cdot)$$ n/a 12912 12
2320.4.ev $$\chi_{2320}(311, \cdot)$$ None 0 12
2320.4.ew $$\chi_{2320}(341, \cdot)$$ n/a 8640 12
2320.4.ey $$\chi_{2320}(141, \cdot)$$ n/a 8640 12
2320.4.fb $$\chi_{2320}(31, \cdot)$$ n/a 2160 12
2320.4.fc $$\chi_{2320}(171, \cdot)$$ n/a 8640 12
2320.4.fe $$\chi_{2320}(123, \cdot)$$ n/a 12912 12
2320.4.fh $$\chi_{2320}(537, \cdot)$$ None 0 12
2320.4.fj $$\chi_{2320}(113, \cdot)$$ n/a 3216 12
2320.4.fk $$\chi_{2320}(187, \cdot)$$ n/a 12912 12
2320.4.fn $$\chi_{2320}(259, \cdot)$$ n/a 12912 12

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(2320))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(2320)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 20}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 16}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 10}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 10}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(58))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(116))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(145))$$$$^{\oplus 5}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(232))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(290))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(464))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(580))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(1160))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2320))$$$$^{\oplus 1}$$