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Properties

Label 560.6
Level 560
Weight 6
Dimension 22634
Nonzero newspaces 28
Sturm bound 110592
Trace bound 11

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Defining parameters

Level: \( N \) = \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 28 \)
Sturm bound: \(110592\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(560))\).

Total New Old
Modular forms 46752 22906 23846
Cusp forms 45408 22634 22774
Eisenstein series 1344 272 1072

Trace form

\( 22634 q - 16 q^{2} - 46 q^{3} - 104 q^{4} - 69 q^{5} + 408 q^{6} + 212 q^{7} + 944 q^{8} + 234 q^{9} + O(q^{10}) \) \( 22634 q - 16 q^{2} - 46 q^{3} - 104 q^{4} - 69 q^{5} + 408 q^{6} + 212 q^{7} + 944 q^{8} + 234 q^{9} - 892 q^{10} - 5110 q^{11} + 8 q^{12} + 716 q^{13} - 216 q^{14} + 2070 q^{15} - 3528 q^{16} - 834 q^{17} - 12560 q^{18} - 6606 q^{19} + 5924 q^{20} - 7414 q^{21} + 17648 q^{22} - 3466 q^{23} + 33464 q^{24} - 12501 q^{25} + 29432 q^{26} + 32720 q^{27} - 22880 q^{28} - 4172 q^{29} - 71852 q^{30} - 38974 q^{31} + 6344 q^{32} + 3802 q^{33} + 91464 q^{34} - 11203 q^{35} - 24384 q^{36} - 71322 q^{37} + 63912 q^{38} - 43552 q^{39} - 86436 q^{40} - 43764 q^{41} - 176720 q^{42} - 25820 q^{43} - 135816 q^{44} + 184720 q^{45} + 217312 q^{46} + 313750 q^{47} + 330536 q^{48} + 648286 q^{49} - 61936 q^{50} - 80650 q^{51} - 245680 q^{52} - 225218 q^{53} - 215416 q^{54} - 94330 q^{55} - 116592 q^{56} - 126012 q^{57} + 111424 q^{58} + 51414 q^{59} - 246172 q^{60} - 158282 q^{61} - 475792 q^{62} + 82328 q^{63} + 240232 q^{64} + 70706 q^{65} + 507416 q^{66} + 271634 q^{67} + 82832 q^{68} + 177876 q^{69} - 384596 q^{70} + 254456 q^{71} + 374776 q^{72} - 48506 q^{73} + 685560 q^{74} - 293001 q^{75} + 137128 q^{76} - 210518 q^{77} - 748960 q^{78} - 1103022 q^{79} - 123172 q^{80} + 152812 q^{81} + 361176 q^{82} + 691176 q^{83} + 591672 q^{84} + 120762 q^{85} + 1517672 q^{86} + 1591232 q^{87} + 1115400 q^{88} + 17914 q^{89} - 1729364 q^{90} - 866144 q^{91} - 1349560 q^{92} - 1025030 q^{93} - 726728 q^{94} - 871719 q^{95} - 2362872 q^{96} - 368388 q^{97} - 2081080 q^{98} + 1856616 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(560))\)

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
560.6.a \(\chi_{560}(1, \cdot)\) 560.6.a.a 1 1
560.6.a.b 1
560.6.a.c 1
560.6.a.d 1
560.6.a.e 1
560.6.a.f 1
560.6.a.g 1
560.6.a.h 1
560.6.a.i 1
560.6.a.j 2
560.6.a.k 2
560.6.a.l 2
560.6.a.m 2
560.6.a.n 2
560.6.a.o 2
560.6.a.p 2
560.6.a.q 3
560.6.a.r 3
560.6.a.s 3
560.6.a.t 3
560.6.a.u 3
560.6.a.v 4
560.6.a.w 4
560.6.a.x 4
560.6.a.y 5
560.6.a.z 5
560.6.b \(\chi_{560}(281, \cdot)\) None 0 1
560.6.e \(\chi_{560}(559, \cdot)\) n/a 120 1
560.6.g \(\chi_{560}(449, \cdot)\) 560.6.g.a 2 1
560.6.g.b 2
560.6.g.c 2
560.6.g.d 10
560.6.g.e 14
560.6.g.f 16
560.6.g.g 20
560.6.g.h 24
560.6.h \(\chi_{560}(391, \cdot)\) None 0 1
560.6.k \(\chi_{560}(111, \cdot)\) 560.6.k.a 24 1
560.6.k.b 56
560.6.l \(\chi_{560}(169, \cdot)\) None 0 1
560.6.n \(\chi_{560}(279, \cdot)\) None 0 1
560.6.q \(\chi_{560}(81, \cdot)\) n/a 160 2
560.6.r \(\chi_{560}(237, \cdot)\) n/a 952 2
560.6.t \(\chi_{560}(43, \cdot)\) n/a 720 2
560.6.w \(\chi_{560}(153, \cdot)\) None 0 2
560.6.x \(\chi_{560}(127, \cdot)\) n/a 180 2
560.6.bb \(\chi_{560}(29, \cdot)\) n/a 720 2
560.6.bc \(\chi_{560}(251, \cdot)\) n/a 640 2
560.6.bd \(\chi_{560}(141, \cdot)\) n/a 480 2
560.6.be \(\chi_{560}(139, \cdot)\) n/a 952 2
560.6.bi \(\chi_{560}(183, \cdot)\) None 0 2
560.6.bj \(\chi_{560}(97, \cdot)\) n/a 236 2
560.6.bl \(\chi_{560}(267, \cdot)\) n/a 720 2
560.6.bn \(\chi_{560}(13, \cdot)\) n/a 952 2
560.6.bq \(\chi_{560}(199, \cdot)\) None 0 2
560.6.bs \(\chi_{560}(31, \cdot)\) n/a 160 2
560.6.bv \(\chi_{560}(9, \cdot)\) None 0 2
560.6.bw \(\chi_{560}(289, \cdot)\) n/a 236 2
560.6.bz \(\chi_{560}(311, \cdot)\) None 0 2
560.6.cb \(\chi_{560}(121, \cdot)\) None 0 2
560.6.cc \(\chi_{560}(159, \cdot)\) n/a 240 2
560.6.cf \(\chi_{560}(107, \cdot)\) n/a 1904 4
560.6.ch \(\chi_{560}(117, \cdot)\) n/a 1904 4
560.6.ci \(\chi_{560}(17, \cdot)\) n/a 472 4
560.6.cl \(\chi_{560}(23, \cdot)\) None 0 4
560.6.co \(\chi_{560}(19, \cdot)\) n/a 1904 4
560.6.cp \(\chi_{560}(221, \cdot)\) n/a 1280 4
560.6.cq \(\chi_{560}(131, \cdot)\) n/a 1280 4
560.6.cr \(\chi_{560}(109, \cdot)\) n/a 1904 4
560.6.cu \(\chi_{560}(207, \cdot)\) n/a 480 4
560.6.cx \(\chi_{560}(73, \cdot)\) None 0 4
560.6.cz \(\chi_{560}(157, \cdot)\) n/a 1904 4
560.6.db \(\chi_{560}(67, \cdot)\) n/a 1904 4

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(560))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(560)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(560))\)\(^{\oplus 1}\)