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Properties

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

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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

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

Display 100 coefficients 10 coefficients

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

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