Properties

 Label 1560.4 Level 1560 Weight 4 Dimension 73684 Nonzero newspaces 60 Sturm bound 516096 Trace bound 31

Defining parameters

 Level: $$N$$ = $$1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$60$$ Sturm bound: $$516096$$ Trace bound: $$31$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(1560))$$.

Total New Old
Modular forms 195840 74212 121628
Cusp forms 191232 73684 117548
Eisenstein series 4608 528 4080

Trace form

 $$73684 q + 8 q^{2} - 12 q^{3} + 48 q^{4} - 16 q^{5} - 112 q^{6} + 32 q^{7} - 304 q^{8} - 184 q^{9} + O(q^{10})$$ $$73684 q + 8 q^{2} - 12 q^{3} + 48 q^{4} - 16 q^{5} - 112 q^{6} + 32 q^{7} - 304 q^{8} - 184 q^{9} + 16 q^{10} - 24 q^{12} - 40 q^{13} + 128 q^{14} - 208 q^{15} - 944 q^{16} - 372 q^{17} - 304 q^{18} - 1488 q^{19} - 1408 q^{20} - 112 q^{21} + 720 q^{22} + 1920 q^{23} + 2168 q^{24} - 1208 q^{25} + 848 q^{26} + 1524 q^{27} + 2192 q^{28} + 1932 q^{29} - 1164 q^{30} - 464 q^{31} - 2352 q^{32} - 2448 q^{33} - 4208 q^{34} - 4056 q^{35} - 3736 q^{36} - 3572 q^{37} + 1040 q^{38} + 1428 q^{39} + 11856 q^{40} + 1500 q^{41} + 11112 q^{42} + 2496 q^{43} + 7936 q^{44} + 910 q^{45} - 3504 q^{46} - 2128 q^{47} - 4520 q^{48} + 4472 q^{49} - 11824 q^{50} + 1224 q^{51} - 22328 q^{52} - 4528 q^{53} - 5456 q^{54} - 4056 q^{55} - 20848 q^{56} + 1720 q^{57} - 13392 q^{58} + 480 q^{59} + 1476 q^{60} + 2684 q^{61} + 5728 q^{62} + 5168 q^{63} + 16272 q^{64} + 3254 q^{65} + 15856 q^{66} - 2608 q^{67} + 5968 q^{68} + 1944 q^{69} + 11456 q^{70} - 352 q^{71} + 10840 q^{72} + 96 q^{73} + 14896 q^{74} - 1288 q^{75} + 17968 q^{76} - 192 q^{77} + 824 q^{78} + 11904 q^{79} + 8416 q^{80} - 13704 q^{81} + 3280 q^{82} + 9376 q^{83} - 15632 q^{84} + 1294 q^{85} - 21344 q^{86} + 27968 q^{87} - 35648 q^{88} + 15568 q^{89} - 9376 q^{90} + 20176 q^{91} - 19408 q^{92} + 5832 q^{93} + 176 q^{94} - 20928 q^{95} + 18280 q^{96} - 14080 q^{97} + 10600 q^{98} - 28104 q^{99} + O(q^{100})$$

Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(1560))$$

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
1560.4.a $$\chi_{1560}(1, \cdot)$$ 1560.4.a.a 1 1
1560.4.a.b 1
1560.4.a.c 1
1560.4.a.d 1
1560.4.a.e 1
1560.4.a.f 2
1560.4.a.g 3
1560.4.a.h 3
1560.4.a.i 3
1560.4.a.j 3
1560.4.a.k 3
1560.4.a.l 4
1560.4.a.m 4
1560.4.a.n 4
1560.4.a.o 5
1560.4.a.p 5
1560.4.a.q 5
1560.4.a.r 5
1560.4.a.s 6
1560.4.a.t 6
1560.4.a.u 6
1560.4.b $$\chi_{1560}(469, \cdot)$$ n/a 432 1
1560.4.e $$\chi_{1560}(131, \cdot)$$ n/a 576 1
1560.4.g $$\chi_{1560}(961, \cdot)$$ 1560.4.g.a 2 1
1560.4.g.b 18
1560.4.g.c 20
1560.4.g.d 20
1560.4.g.e 24
1560.4.h $$\chi_{1560}(1559, \cdot)$$ None 0 1
1560.4.k $$\chi_{1560}(911, \cdot)$$ None 0 1
1560.4.l $$\chi_{1560}(1249, \cdot)$$ n/a 108 1
1560.4.n $$\chi_{1560}(779, \cdot)$$ n/a 1000 1
1560.4.q $$\chi_{1560}(181, \cdot)$$ n/a 336 1
1560.4.r $$\chi_{1560}(649, \cdot)$$ n/a 124 1
1560.4.u $$\chi_{1560}(311, \cdot)$$ None 0 1
1560.4.w $$\chi_{1560}(781, \cdot)$$ n/a 288 1
1560.4.x $$\chi_{1560}(1379, \cdot)$$ n/a 864 1
1560.4.ba $$\chi_{1560}(1091, \cdot)$$ n/a 672 1
1560.4.bb $$\chi_{1560}(1429, \cdot)$$ n/a 504 1
1560.4.bd $$\chi_{1560}(599, \cdot)$$ None 0 1
1560.4.bg $$\chi_{1560}(601, \cdot)$$ n/a 168 2
1560.4.bh $$\chi_{1560}(73, \cdot)$$ n/a 252 2
1560.4.bi $$\chi_{1560}(83, \cdot)$$ n/a 2000 2
1560.4.bn $$\chi_{1560}(853, \cdot)$$ n/a 1008 2
1560.4.bo $$\chi_{1560}(47, \cdot)$$ None 0 2
1560.4.bq $$\chi_{1560}(77, \cdot)$$ n/a 2000 2
1560.4.br $$\chi_{1560}(833, \cdot)$$ n/a 432 2
1560.4.bu $$\chi_{1560}(703, \cdot)$$ None 0 2
1560.4.bv $$\chi_{1560}(883, \cdot)$$ n/a 1008 2
1560.4.by $$\chi_{1560}(1409, \cdot)$$ n/a 504 2
1560.4.bz $$\chi_{1560}(629, \cdot)$$ n/a 2000 2
1560.4.cb $$\chi_{1560}(811, \cdot)$$ n/a 672 2
1560.4.ce $$\chi_{1560}(31, \cdot)$$ None 0 2
1560.4.cg $$\chi_{1560}(499, \cdot)$$ n/a 1008 2
1560.4.ch $$\chi_{1560}(1279, \cdot)$$ None 0 2
1560.4.cj $$\chi_{1560}(161, \cdot)$$ n/a 336 2
1560.4.cm $$\chi_{1560}(941, \cdot)$$ n/a 1344 2
1560.4.cn $$\chi_{1560}(103, \cdot)$$ None 0 2
1560.4.cq $$\chi_{1560}(547, \cdot)$$ n/a 864 2
1560.4.cr $$\chi_{1560}(53, \cdot)$$ n/a 1728 2
1560.4.cu $$\chi_{1560}(233, \cdot)$$ n/a 504 2
1560.4.cx $$\chi_{1560}(203, \cdot)$$ n/a 2000 2
1560.4.cy $$\chi_{1560}(697, \cdot)$$ n/a 252 2
1560.4.cz $$\chi_{1560}(983, \cdot)$$ None 0 2
1560.4.da $$\chi_{1560}(733, \cdot)$$ n/a 1008 2
1560.4.df $$\chi_{1560}(1199, \cdot)$$ None 0 2
1560.4.dh $$\chi_{1560}(589, \cdot)$$ n/a 1008 2
1560.4.di $$\chi_{1560}(251, \cdot)$$ n/a 1344 2
1560.4.dl $$\chi_{1560}(419, \cdot)$$ n/a 2000 2
1560.4.dm $$\chi_{1560}(61, \cdot)$$ n/a 672 2
1560.4.do $$\chi_{1560}(1031, \cdot)$$ None 0 2
1560.4.dr $$\chi_{1560}(49, \cdot)$$ n/a 248 2
1560.4.ds $$\chi_{1560}(901, \cdot)$$ n/a 672 2
1560.4.dv $$\chi_{1560}(179, \cdot)$$ n/a 2000 2
1560.4.dx $$\chi_{1560}(289, \cdot)$$ n/a 256 2
1560.4.dy $$\chi_{1560}(191, \cdot)$$ None 0 2
1560.4.eb $$\chi_{1560}(719, \cdot)$$ None 0 2
1560.4.ec $$\chi_{1560}(121, \cdot)$$ n/a 168 2
1560.4.ee $$\chi_{1560}(731, \cdot)$$ n/a 1344 2
1560.4.eh $$\chi_{1560}(1069, \cdot)$$ n/a 1008 2
1560.4.ek $$\chi_{1560}(1007, \cdot)$$ None 0 4
1560.4.el $$\chi_{1560}(37, \cdot)$$ n/a 2016 4
1560.4.em $$\chi_{1560}(227, \cdot)$$ n/a 4000 4
1560.4.en $$\chi_{1560}(817, \cdot)$$ n/a 504 4
1560.4.eq $$\chi_{1560}(17, \cdot)$$ n/a 1008 4
1560.4.et $$\chi_{1560}(653, \cdot)$$ n/a 4000 4
1560.4.eu $$\chi_{1560}(523, \cdot)$$ n/a 2016 4
1560.4.ex $$\chi_{1560}(127, \cdot)$$ None 0 4
1560.4.ez $$\chi_{1560}(461, \cdot)$$ n/a 2688 4
1560.4.fa $$\chi_{1560}(41, \cdot)$$ n/a 672 4
1560.4.fc $$\chi_{1560}(319, \cdot)$$ None 0 4
1560.4.ff $$\chi_{1560}(19, \cdot)$$ n/a 2016 4
1560.4.fh $$\chi_{1560}(271, \cdot)$$ None 0 4
1560.4.fi $$\chi_{1560}(331, \cdot)$$ n/a 1344 4
1560.4.fk $$\chi_{1560}(149, \cdot)$$ n/a 4000 4
1560.4.fn $$\chi_{1560}(89, \cdot)$$ n/a 1008 4
1560.4.fp $$\chi_{1560}(43, \cdot)$$ n/a 2016 4
1560.4.fq $$\chi_{1560}(367, \cdot)$$ None 0 4
1560.4.ft $$\chi_{1560}(113, \cdot)$$ n/a 1008 4
1560.4.fu $$\chi_{1560}(173, \cdot)$$ n/a 4000 4
1560.4.fw $$\chi_{1560}(877, \cdot)$$ n/a 2016 4
1560.4.fx $$\chi_{1560}(167, \cdot)$$ None 0 4
1560.4.gc $$\chi_{1560}(97, \cdot)$$ n/a 504 4
1560.4.gd $$\chi_{1560}(947, \cdot)$$ n/a 4000 4

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

Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(1560))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(1560)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 16}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 16}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(130))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(260))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(390))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(520))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(780))$$$$^{\oplus 2}$$