Properties

Label 280.6
Level 280
Weight 6
Dimension 5634
Nonzero newspaces 18
Sturm bound 27648
Trace bound 7

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Defining parameters

Level: \( N \) = \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(27648\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(280))\).

Total New Old
Modular forms 11808 5754 6054
Cusp forms 11232 5634 5598
Eisenstein series 576 120 456

Trace form

\( 5634q - 12q^{2} + 76q^{3} + 76q^{4} - 66q^{5} - 484q^{6} + 60q^{7} - 1008q^{8} - 366q^{9} + O(q^{10}) \) \( 5634q - 12q^{2} + 76q^{3} + 76q^{4} - 66q^{5} - 484q^{6} + 60q^{7} - 1008q^{8} - 366q^{9} + 1254q^{10} + 576q^{11} + 4356q^{12} + 1584q^{13} - 2028q^{14} + 1856q^{15} - 10228q^{16} - 5616q^{17} + 920q^{18} - 10948q^{19} - 1900q^{20} + 11032q^{21} + 11060q^{22} + 18672q^{23} + 1724q^{24} + 19976q^{25} + 10312q^{26} - 25112q^{27} - 59396q^{28} - 18636q^{29} - 32002q^{30} - 3384q^{31} + 15528q^{32} + 37884q^{33} + 35444q^{34} - 6050q^{35} + 38668q^{36} - 7760q^{37} + 55720q^{38} + 46248q^{39} + 131784q^{40} - 6348q^{41} + 68356q^{42} - 127216q^{43} - 136988q^{44} + 56260q^{45} - 294640q^{46} + 108688q^{47} - 291972q^{48} - 133358q^{49} + 91736q^{50} - 39064q^{51} + 362856q^{52} - 28616q^{53} + 670748q^{54} - 110688q^{55} + 235424q^{56} - 188304q^{57} - 133752q^{58} - 303772q^{59} - 421712q^{60} - 8532q^{61} - 441992q^{62} + 284292q^{63} - 294788q^{64} - 41312q^{65} - 220796q^{66} - 49528q^{67} - 345236q^{68} + 36056q^{69} + 262046q^{70} + 579760q^{71} + 752072q^{72} + 422488q^{73} + 772644q^{74} + 197448q^{75} + 683692q^{76} + 20980q^{77} - 13184q^{78} - 660528q^{79} - 95764q^{80} - 896154q^{81} - 533748q^{82} - 517180q^{83} - 1007076q^{84} - 144868q^{85} - 635660q^{86} + 191224q^{87} - 628892q^{88} + 1029832q^{89} + 315912q^{90} + 759108q^{91} + 1033500q^{92} + 715876q^{93} + 1387596q^{94} - 420708q^{95} + 200908q^{96} + 31540q^{97} - 468980q^{98} - 2009040q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(280))\)

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
280.6.a \(\chi_{280}(1, \cdot)\) 280.6.a.a 1 1
280.6.a.b 1
280.6.a.c 2
280.6.a.d 2
280.6.a.e 3
280.6.a.f 3
280.6.a.g 4
280.6.a.h 4
280.6.a.i 5
280.6.a.j 5
280.6.b \(\chi_{280}(141, \cdot)\) n/a 120 1
280.6.e \(\chi_{280}(279, \cdot)\) None 0 1
280.6.g \(\chi_{280}(169, \cdot)\) 280.6.g.a 20 1
280.6.g.b 24
280.6.h \(\chi_{280}(251, \cdot)\) n/a 160 1
280.6.k \(\chi_{280}(111, \cdot)\) None 0 1
280.6.l \(\chi_{280}(29, \cdot)\) n/a 180 1
280.6.n \(\chi_{280}(139, \cdot)\) n/a 236 1
280.6.q \(\chi_{280}(81, \cdot)\) 280.6.q.a 18 2
280.6.q.b 20
280.6.q.c 20
280.6.q.d 22
280.6.s \(\chi_{280}(13, \cdot)\) n/a 472 2
280.6.t \(\chi_{280}(127, \cdot)\) None 0 2
280.6.w \(\chi_{280}(43, \cdot)\) n/a 360 2
280.6.x \(\chi_{280}(97, \cdot)\) n/a 120 2
280.6.ba \(\chi_{280}(19, \cdot)\) n/a 472 2
280.6.bc \(\chi_{280}(31, \cdot)\) None 0 2
280.6.bf \(\chi_{280}(109, \cdot)\) n/a 472 2
280.6.bg \(\chi_{280}(9, \cdot)\) n/a 120 2
280.6.bj \(\chi_{280}(131, \cdot)\) n/a 320 2
280.6.bl \(\chi_{280}(221, \cdot)\) n/a 320 2
280.6.bm \(\chi_{280}(159, \cdot)\) None 0 2
280.6.bo \(\chi_{280}(17, \cdot)\) n/a 240 4
280.6.br \(\chi_{280}(67, \cdot)\) n/a 944 4
280.6.bs \(\chi_{280}(23, \cdot)\) None 0 4
280.6.bv \(\chi_{280}(117, \cdot)\) n/a 944 4

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(280))\) into lower level spaces

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