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

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

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

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