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Properties

Label 140.3
Level 140
Weight 3
Dimension 560
Nonzero newspaces 12
Newform subspaces 17
Sturm bound 3456
Trace bound 3

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Defining parameters

Level: \( N \) = \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 17 \)
Sturm bound: \(3456\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(140))\).

Total New Old
Modular forms 1272 624 648
Cusp forms 1032 560 472
Eisenstein series 240 64 176

Trace form

\( 560 q - 2 q^{2} - 10 q^{3} + 2 q^{4} - q^{5} + 20 q^{6} + 22 q^{7} + 34 q^{8} + 76 q^{9} + O(q^{10}) \) \( 560 q - 2 q^{2} - 10 q^{3} + 2 q^{4} - q^{5} + 20 q^{6} + 22 q^{7} + 34 q^{8} + 76 q^{9} + 6 q^{10} + 14 q^{11} - 56 q^{12} - 4 q^{13} - 86 q^{14} - 58 q^{15} - 186 q^{16} - 70 q^{17} - 254 q^{18} - 54 q^{19} - 44 q^{20} + 74 q^{21} - 56 q^{22} + 194 q^{23} + 120 q^{24} + 25 q^{25} + 192 q^{26} + 188 q^{27} + 82 q^{28} - 16 q^{29} + 46 q^{30} + 170 q^{31} + 158 q^{32} - 206 q^{33} + 180 q^{34} - 65 q^{35} + 350 q^{36} - 502 q^{37} + 212 q^{38} - 252 q^{39} + 144 q^{40} - 88 q^{41} - 168 q^{42} - 236 q^{43} - 308 q^{44} - 130 q^{45} - 316 q^{46} - 150 q^{47} - 840 q^{48} - 188 q^{49} - 490 q^{50} - 494 q^{51} - 772 q^{52} - 154 q^{53} - 944 q^{54} - 216 q^{55} - 726 q^{56} - 100 q^{57} - 312 q^{58} - 198 q^{59} - 764 q^{60} - 466 q^{61} + 160 q^{62} - 458 q^{63} + 134 q^{64} - 560 q^{65} - 4 q^{66} + 18 q^{67} + 140 q^{68} - 296 q^{69} + 74 q^{70} + 40 q^{71} + 66 q^{72} + 458 q^{73} - 24 q^{74} + 841 q^{75} - 12 q^{76} + 662 q^{77} + 808 q^{78} + 518 q^{79} + 1152 q^{80} + 1674 q^{81} + 944 q^{82} + 924 q^{83} + 1648 q^{84} + 1378 q^{85} + 704 q^{86} + 1112 q^{87} + 1012 q^{88} + 1026 q^{89} + 1236 q^{90} + 780 q^{91} + 1320 q^{92} + 898 q^{93} + 544 q^{94} + 469 q^{95} + 788 q^{96} - 1116 q^{97} + 350 q^{98} - 240 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(140))\)

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
140.3.b \(\chi_{140}(71, \cdot)\) 140.3.b.a 24 1
140.3.d \(\chi_{140}(41, \cdot)\) 140.3.d.a 4 1
140.3.f \(\chi_{140}(99, \cdot)\) 140.3.f.a 36 1
140.3.h \(\chi_{140}(69, \cdot)\) 140.3.h.a 2 1
140.3.h.b 2
140.3.h.c 4
140.3.j \(\chi_{140}(27, \cdot)\) 140.3.j.a 88 2
140.3.l \(\chi_{140}(57, \cdot)\) 140.3.l.a 4 2
140.3.l.b 8
140.3.n \(\chi_{140}(89, \cdot)\) 140.3.n.a 16 2
140.3.p \(\chi_{140}(39, \cdot)\) 140.3.p.a 4 2
140.3.p.b 4
140.3.p.c 80
140.3.r \(\chi_{140}(61, \cdot)\) 140.3.r.a 12 2
140.3.t \(\chi_{140}(11, \cdot)\) 140.3.t.a 64 2
140.3.v \(\chi_{140}(37, \cdot)\) 140.3.v.a 32 4
140.3.x \(\chi_{140}(3, \cdot)\) 140.3.x.a 176 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(140))\) into lower level spaces

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