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Properties

Label 140.4
Level 140
Weight 4
Dimension 854
Nonzero newspaces 12
Newform subspaces 25
Sturm bound 4608
Trace bound 5

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Defining parameters

Level: \( N \) = \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 25 \)
Sturm bound: \(4608\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(140))\).

Total New Old
Modular forms 1848 910 938
Cusp forms 1608 854 754
Eisenstein series 240 56 184

Trace form

\( 854 q - 2 q^{2} + 4 q^{3} - 6 q^{4} - 60 q^{5} - 40 q^{6} - 32 q^{7} - 26 q^{8} + 122 q^{9} + O(q^{10}) \) \( 854 q - 2 q^{2} + 4 q^{3} - 6 q^{4} - 60 q^{5} - 40 q^{6} - 32 q^{7} - 26 q^{8} + 122 q^{9} + 148 q^{10} + 208 q^{11} + 484 q^{12} + 20 q^{13} + 306 q^{14} - 152 q^{15} - 218 q^{16} + 88 q^{17} - 666 q^{18} - 388 q^{19} - 644 q^{20} - 1276 q^{21} - 996 q^{22} - 264 q^{23} - 708 q^{24} - 298 q^{25} + 104 q^{26} + 736 q^{27} - 422 q^{28} + 2196 q^{29} + 1568 q^{30} + 400 q^{31} - 422 q^{32} + 416 q^{33} + 958 q^{35} + 190 q^{36} - 1256 q^{37} + 28 q^{38} - 664 q^{39} - 2136 q^{40} - 92 q^{41} + 2836 q^{42} + 176 q^{43} + 4152 q^{44} - 1436 q^{45} + 5156 q^{46} - 1224 q^{47} + 5428 q^{48} - 1510 q^{49} + 3330 q^{50} + 776 q^{51} - 1380 q^{52} + 112 q^{53} - 6564 q^{54} + 1552 q^{55} - 3722 q^{56} + 2264 q^{57} - 4416 q^{58} + 844 q^{59} - 6260 q^{60} + 3760 q^{61} - 6296 q^{62} - 872 q^{63} - 2106 q^{64} + 644 q^{65} + 3672 q^{66} - 2632 q^{67} + 8168 q^{68} - 5816 q^{69} - 2048 q^{70} - 6192 q^{71} + 4974 q^{72} - 8976 q^{73} - 2652 q^{74} - 7132 q^{75} - 5512 q^{76} + 1344 q^{77} - 14280 q^{78} + 3464 q^{79} - 6808 q^{80} - 4002 q^{81} - 6028 q^{82} - 132 q^{83} - 7812 q^{84} - 684 q^{85} + 124 q^{86} + 840 q^{87} + 3792 q^{88} + 10484 q^{89} + 6888 q^{90} + 2564 q^{91} + 10388 q^{92} + 14968 q^{93} + 13548 q^{94} + 4180 q^{95} + 21368 q^{96} + 15032 q^{97} + 18494 q^{98} + 14000 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(140))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
140.4.a \(\chi_{140}(1, \cdot)\) 140.4.a.a 1 1
140.4.a.b 1
140.4.a.c 1
140.4.a.d 1
140.4.a.e 1
140.4.a.f 1
140.4.c \(\chi_{140}(139, \cdot)\) 140.4.c.a 4 1
140.4.c.b 64
140.4.e \(\chi_{140}(29, \cdot)\) 140.4.e.a 2 1
140.4.e.b 2
140.4.e.c 4
140.4.g \(\chi_{140}(111, \cdot)\) 140.4.g.a 48 1
140.4.i \(\chi_{140}(81, \cdot)\) 140.4.i.a 2 2
140.4.i.b 2
140.4.i.c 4
140.4.i.d 4
140.4.i.e 4
140.4.k \(\chi_{140}(43, \cdot)\) 140.4.k.a 108 2
140.4.m \(\chi_{140}(13, \cdot)\) 140.4.m.a 24 2
140.4.o \(\chi_{140}(31, \cdot)\) 140.4.o.a 96 2
140.4.q \(\chi_{140}(9, \cdot)\) 140.4.q.a 24 2
140.4.s \(\chi_{140}(19, \cdot)\) 140.4.s.a 8 2
140.4.s.b 128
140.4.u \(\chi_{140}(17, \cdot)\) 140.4.u.a 48 4
140.4.w \(\chi_{140}(23, \cdot)\) 140.4.w.a 272 4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(140))\) into lower level spaces

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