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Properties

Label 560.3
Level 560
Weight 3
Dimension 8974
Nonzero newspaces 28
Sturm bound 55296
Trace bound 11

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Defining parameters

Level: \( N \) = \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 28 \)
Sturm bound: \(55296\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(560))\).

Total New Old
Modular forms 19104 9242 9862
Cusp forms 17760 8974 8786
Eisenstein series 1344 268 1076

Trace form

\( 8974 q - 16 q^{2} - 14 q^{3} - 40 q^{4} - 41 q^{5} - 72 q^{6} - 20 q^{7} - 16 q^{8} + 30 q^{9} + O(q^{10}) \) \( 8974 q - 16 q^{2} - 14 q^{3} - 40 q^{4} - 41 q^{5} - 72 q^{6} - 20 q^{7} - 16 q^{8} + 30 q^{9} + 52 q^{10} - 102 q^{11} + 200 q^{12} - 32 q^{13} + 8 q^{14} - 138 q^{15} - 200 q^{16} - 186 q^{17} - 304 q^{18} + 22 q^{19} - 188 q^{20} - 222 q^{21} - 240 q^{22} + 186 q^{23} + 184 q^{24} + 15 q^{25} + 344 q^{26} + 484 q^{27} + 224 q^{28} + 340 q^{29} + 660 q^{30} + 290 q^{31} + 584 q^{32} + 674 q^{33} + 328 q^{34} + 71 q^{35} + 64 q^{36} + 294 q^{37} + 264 q^{38} - 572 q^{39} - 100 q^{40} - 72 q^{41} + 560 q^{42} - 464 q^{43} + 568 q^{44} - 74 q^{45} + 256 q^{46} - 198 q^{47} + 424 q^{48} - 426 q^{49} - 624 q^{50} + 258 q^{51} + 208 q^{52} + 342 q^{53} - 120 q^{54} + 212 q^{55} - 560 q^{56} - 556 q^{57} - 1216 q^{58} + 630 q^{59} - 1436 q^{60} - 530 q^{61} - 2096 q^{62} + 124 q^{63} - 2008 q^{64} - 200 q^{65} - 3560 q^{66} + 290 q^{67} - 2352 q^{68} - 1528 q^{69} - 1412 q^{70} - 324 q^{71} - 3016 q^{72} - 522 q^{73} - 1256 q^{74} + 481 q^{75} - 1176 q^{76} - 874 q^{77} - 608 q^{78} - 354 q^{79} + 604 q^{80} - 56 q^{81} + 1624 q^{82} + 88 q^{83} + 1208 q^{84} - 886 q^{85} + 1928 q^{86} - 632 q^{87} + 1544 q^{88} + 18 q^{89} + 1868 q^{90} + 1132 q^{91} + 968 q^{92} + 234 q^{93} - 584 q^{94} + 61 q^{95} - 1784 q^{96} + 880 q^{97} - 1528 q^{98} + 2532 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(560))\)

We only show spaces with odd 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
560.3.c \(\chi_{560}(489, \cdot)\) None 0 1
560.3.d \(\chi_{560}(351, \cdot)\) 560.3.d.a 8 1
560.3.d.b 16
560.3.f \(\chi_{560}(321, \cdot)\) 560.3.f.a 2 1
560.3.f.b 2
560.3.f.c 4
560.3.f.d 8
560.3.f.e 16
560.3.i \(\chi_{560}(519, \cdot)\) None 0 1
560.3.j \(\chi_{560}(239, \cdot)\) 560.3.j.a 12 1
560.3.j.b 24
560.3.m \(\chi_{560}(41, \cdot)\) None 0 1
560.3.o \(\chi_{560}(71, \cdot)\) None 0 1
560.3.p \(\chi_{560}(209, \cdot)\) 560.3.p.a 1 1
560.3.p.b 1
560.3.p.c 2
560.3.p.d 2
560.3.p.e 4
560.3.p.f 4
560.3.p.g 8
560.3.p.h 24
560.3.s \(\chi_{560}(197, \cdot)\) n/a 288 2
560.3.u \(\chi_{560}(27, \cdot)\) n/a 376 2
560.3.v \(\chi_{560}(223, \cdot)\) 560.3.v.a 32 2
560.3.v.b 64
560.3.y \(\chi_{560}(57, \cdot)\) None 0 2
560.3.z \(\chi_{560}(181, \cdot)\) n/a 256 2
560.3.ba \(\chi_{560}(99, \cdot)\) n/a 288 2
560.3.bf \(\chi_{560}(69, \cdot)\) n/a 376 2
560.3.bg \(\chi_{560}(211, \cdot)\) n/a 192 2
560.3.bh \(\chi_{560}(113, \cdot)\) 560.3.bh.a 4 2
560.3.bh.b 4
560.3.bh.c 8
560.3.bh.d 8
560.3.bh.e 12
560.3.bh.f 16
560.3.bh.g 20
560.3.bk \(\chi_{560}(167, \cdot)\) None 0 2
560.3.bm \(\chi_{560}(307, \cdot)\) n/a 376 2
560.3.bo \(\chi_{560}(477, \cdot)\) n/a 288 2
560.3.bp \(\chi_{560}(151, \cdot)\) None 0 2
560.3.br \(\chi_{560}(129, \cdot)\) 560.3.br.a 12 2
560.3.br.b 16
560.3.br.c 16
560.3.br.d 48
560.3.bt \(\chi_{560}(79, \cdot)\) 560.3.bt.a 8 2
560.3.bt.b 24
560.3.bt.c 32
560.3.bt.d 32
560.3.bu \(\chi_{560}(201, \cdot)\) None 0 2
560.3.bx \(\chi_{560}(241, \cdot)\) 560.3.bx.a 8 2
560.3.bx.b 12
560.3.bx.c 12
560.3.bx.d 32
560.3.by \(\chi_{560}(39, \cdot)\) None 0 2
560.3.ca \(\chi_{560}(89, \cdot)\) None 0 2
560.3.cd \(\chi_{560}(191, \cdot)\) 560.3.cd.a 20 2
560.3.cd.b 20
560.3.cd.c 24
560.3.ce \(\chi_{560}(227, \cdot)\) n/a 752 4
560.3.cg \(\chi_{560}(53, \cdot)\) n/a 752 4
560.3.cj \(\chi_{560}(87, \cdot)\) None 0 4
560.3.ck \(\chi_{560}(177, \cdot)\) n/a 184 4
560.3.cm \(\chi_{560}(11, \cdot)\) n/a 512 4
560.3.cn \(\chi_{560}(229, \cdot)\) n/a 752 4
560.3.cs \(\chi_{560}(179, \cdot)\) n/a 752 4
560.3.ct \(\chi_{560}(61, \cdot)\) n/a 512 4
560.3.cv \(\chi_{560}(137, \cdot)\) None 0 4
560.3.cw \(\chi_{560}(47, \cdot)\) n/a 192 4
560.3.cy \(\chi_{560}(37, \cdot)\) n/a 752 4
560.3.da \(\chi_{560}(3, \cdot)\) n/a 752 4

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(560))\) into lower level spaces

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