↑

Properties

Label 280.5
Level 280
Weight 5
Dimension 4492
Nonzero newspaces 18
Sturm bound 23040
Trace bound 6

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(23040\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(280))\).

Total New Old
Modular forms 9504 4612 4892
Cusp forms 8928 4492 4436
Eisenstein series 576 120 456

Trace form

\( 4492 q + 4 q^{2} - 12 q^{3} - 52 q^{4} - 48 q^{5} - 292 q^{6} + 72 q^{7} + 592 q^{8} + 188 q^{9} + O(q^{10}) \) \( 4492 q + 4 q^{2} - 12 q^{3} - 52 q^{4} - 48 q^{5} - 292 q^{6} + 72 q^{7} + 592 q^{8} + 188 q^{9} + 470 q^{10} - 268 q^{11} - 924 q^{12} - 40 q^{13} - 1148 q^{14} - 1708 q^{15} - 116 q^{16} - 1240 q^{17} + 1208 q^{18} + 5164 q^{19} + 1724 q^{20} + 1888 q^{21} - 2044 q^{22} - 484 q^{23} - 3460 q^{24} + 4664 q^{25} - 3368 q^{26} - 6816 q^{27} + 3468 q^{28} - 834 q^{30} + 2908 q^{31} + 12184 q^{32} - 936 q^{33} + 12340 q^{34} + 730 q^{35} + 19580 q^{36} - 4712 q^{37} - 7624 q^{38} - 3216 q^{39} - 15840 q^{40} + 15504 q^{41} - 30060 q^{42} + 6408 q^{43} - 33052 q^{44} + 13888 q^{45} + 12272 q^{46} - 1012 q^{47} + 38428 q^{48} - 6484 q^{49} + 8872 q^{50} - 39156 q^{51} + 28936 q^{52} - 20520 q^{53} - 16196 q^{54} - 10904 q^{55} - 15136 q^{56} - 21248 q^{57} - 27640 q^{58} - 6244 q^{59} - 32952 q^{60} + 18288 q^{61} - 53704 q^{62} + 55984 q^{63} - 6436 q^{64} + 46972 q^{65} + 46852 q^{66} + 75252 q^{67} + 104508 q^{68} + 72318 q^{70} - 1112 q^{71} + 83800 q^{72} - 47256 q^{73} - 57148 q^{74} - 33970 q^{75} - 96788 q^{76} - 35376 q^{77} - 102752 q^{78} - 19884 q^{79} - 42492 q^{80} + 9684 q^{81} - 20436 q^{82} + 31200 q^{83} + 19580 q^{84} + 43080 q^{85} + 5780 q^{86} - 9592 q^{87} - 45532 q^{88} + 56480 q^{89} - 109648 q^{90} - 13448 q^{91} + 4476 q^{92} + 34608 q^{93} - 25460 q^{94} - 15314 q^{95} - 104468 q^{96} - 48904 q^{97} + 33324 q^{98} + 66864 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(280))\)

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
280.5.c \(\chi_{280}(69, \cdot)\) n/a 188 1
280.5.d \(\chi_{280}(71, \cdot)\) None 0 1
280.5.f \(\chi_{280}(41, \cdot)\) 280.5.f.a 32 1
280.5.i \(\chi_{280}(99, \cdot)\) n/a 144 1
280.5.j \(\chi_{280}(239, \cdot)\) None 0 1
280.5.m \(\chi_{280}(181, \cdot)\) n/a 128 1
280.5.o \(\chi_{280}(211, \cdot)\) 280.5.o.a 96 1
280.5.p \(\chi_{280}(209, \cdot)\) 280.5.p.a 48 1
280.5.r \(\chi_{280}(167, \cdot)\) None 0 2
280.5.u \(\chi_{280}(197, \cdot)\) n/a 288 2
280.5.v \(\chi_{280}(57, \cdot)\) 280.5.v.a 36 2
280.5.v.b 36
280.5.y \(\chi_{280}(27, \cdot)\) n/a 376 2
280.5.z \(\chi_{280}(11, \cdot)\) n/a 256 2
280.5.bb \(\chi_{280}(89, \cdot)\) 280.5.bb.a 96 2
280.5.bd \(\chi_{280}(39, \cdot)\) None 0 2
280.5.be \(\chi_{280}(61, \cdot)\) n/a 256 2
280.5.bh \(\chi_{280}(201, \cdot)\) 280.5.bh.a 64 2
280.5.bi \(\chi_{280}(179, \cdot)\) n/a 376 2
280.5.bk \(\chi_{280}(229, \cdot)\) n/a 376 2
280.5.bn \(\chi_{280}(151, \cdot)\) None 0 2
280.5.bp \(\chi_{280}(3, \cdot)\) n/a 752 4
280.5.bq \(\chi_{280}(137, \cdot)\) n/a 192 4
280.5.bt \(\chi_{280}(37, \cdot)\) n/a 752 4
280.5.bu \(\chi_{280}(47, \cdot)\) None 0 4

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(280))\) into lower level spaces

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