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Properties

Label 140.5
Level 140
Weight 5
Dimension 1152
Nonzero newspaces 12
Newform subspaces 16
Sturm bound 5760
Trace bound 2

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Defining parameters

Level: \( N \) = \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 16 \)
Sturm bound: \(5760\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(140))\).

Total New Old
Modular forms 2424 1216 1208
Cusp forms 2184 1152 1032
Eisenstein series 240 64 176

Trace form

\( 1152 q - 18 q^{2} + 2 q^{3} + 66 q^{4} + q^{5} - 76 q^{6} - 214 q^{7} - 174 q^{8} + 16 q^{9} + O(q^{10}) \) \( 1152 q - 18 q^{2} + 2 q^{3} + 66 q^{4} + q^{5} - 76 q^{6} - 214 q^{7} - 174 q^{8} + 16 q^{9} + 114 q^{10} + 258 q^{11} - 296 q^{12} + 16 q^{13} + 826 q^{14} - 310 q^{15} + 2822 q^{16} + 378 q^{17} + 586 q^{18} + 1494 q^{19} - 1340 q^{20} - 1282 q^{21} - 760 q^{22} - 1818 q^{23} - 2712 q^{24} - 3545 q^{25} + 960 q^{26} - 5500 q^{27} - 2686 q^{28} + 2648 q^{29} - 14 q^{30} + 8566 q^{31} + 3342 q^{32} + 9694 q^{33} - 972 q^{34} + 1041 q^{35} + 6734 q^{36} - 710 q^{37} + 3564 q^{38} - 924 q^{39} - 8904 q^{40} - 15040 q^{41} - 14424 q^{42} + 6476 q^{43} - 12756 q^{44} - 6250 q^{45} - 6532 q^{46} + 12294 q^{47} + 22200 q^{48} + 11200 q^{49} + 30822 q^{50} - 13634 q^{51} + 32092 q^{52} - 15762 q^{53} + 30856 q^{54} - 15336 q^{55} - 11702 q^{56} + 8420 q^{57} - 1176 q^{58} + 14526 q^{59} - 12020 q^{60} - 31462 q^{61} - 51360 q^{62} + 9538 q^{63} - 48666 q^{64} + 27528 q^{65} - 64972 q^{66} + 21462 q^{67} - 23700 q^{68} + 75448 q^{69} - 1722 q^{70} + 6792 q^{71} + 77346 q^{72} - 8630 q^{73} + 94272 q^{74} - 34037 q^{75} + 71988 q^{76} - 65382 q^{77} + 50920 q^{78} - 24206 q^{79} - 27440 q^{80} - 26202 q^{81} - 11648 q^{82} - 19740 q^{83} - 56816 q^{84} - 15670 q^{85} - 121456 q^{86} + 5552 q^{87} - 122380 q^{88} - 5578 q^{89} - 38508 q^{90} + 19380 q^{91} - 64248 q^{92} - 3650 q^{93} - 8472 q^{94} - 38625 q^{95} + 82100 q^{96} - 62016 q^{97} + 66894 q^{98} - 101616 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(140))\)

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
140.5.b \(\chi_{140}(71, \cdot)\) 140.5.b.a 48 1
140.5.d \(\chi_{140}(41, \cdot)\) 140.5.d.a 12 1
140.5.f \(\chi_{140}(99, \cdot)\) 140.5.f.a 72 1
140.5.h \(\chi_{140}(69, \cdot)\) 140.5.h.a 2 1
140.5.h.b 2
140.5.h.c 12
140.5.j \(\chi_{140}(27, \cdot)\) 140.5.j.a 184 2
140.5.l \(\chi_{140}(57, \cdot)\) 140.5.l.a 24 2
140.5.n \(\chi_{140}(89, \cdot)\) 140.5.n.a 32 2
140.5.p \(\chi_{140}(39, \cdot)\) 140.5.p.a 4 2
140.5.p.b 4
140.5.p.c 176
140.5.r \(\chi_{140}(61, \cdot)\) 140.5.r.a 20 2
140.5.t \(\chi_{140}(11, \cdot)\) 140.5.t.a 128 2
140.5.v \(\chi_{140}(37, \cdot)\) 140.5.v.a 64 4
140.5.x \(\chi_{140}(3, \cdot)\) 140.5.x.a 368 4

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(140))\) into lower level spaces

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