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Properties

Label 160.3
Level 160
Weight 3
Dimension 762
Nonzero newspaces 10
Newform subspaces 19
Sturm bound 4608
Trace bound 9

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Defining parameters

Level: \( N \) = \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 19 \)
Sturm bound: \(4608\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(160))\).

Total New Old
Modular forms 1664 822 842
Cusp forms 1408 762 646
Eisenstein series 256 60 196

Trace form

\( 762 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 16 q^{5} - 24 q^{6} - 4 q^{7} - 8 q^{8} + 22 q^{9} + O(q^{10}) \) \( 762 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 16 q^{5} - 24 q^{6} - 4 q^{7} - 8 q^{8} + 22 q^{9} + 28 q^{10} + 12 q^{11} + 88 q^{12} + 48 q^{13} + 24 q^{14} - 4 q^{15} - 64 q^{16} - 84 q^{17} - 128 q^{18} - 68 q^{19} - 92 q^{20} - 152 q^{21} - 304 q^{22} + 124 q^{23} - 432 q^{24} + 22 q^{25} - 224 q^{26} + 280 q^{27} - 128 q^{28} + 128 q^{29} - 36 q^{30} + 104 q^{31} + 32 q^{32} + 160 q^{33} + 80 q^{34} - 8 q^{35} + 640 q^{36} + 192 q^{37} + 776 q^{38} - 392 q^{39} + 392 q^{40} + 44 q^{41} + 832 q^{42} - 296 q^{43} + 360 q^{44} - 188 q^{45} + 40 q^{46} - 188 q^{47} - 112 q^{48} - 366 q^{49} - 324 q^{50} - 672 q^{51} - 856 q^{52} - 64 q^{53} - 1200 q^{54} - 364 q^{55} - 1136 q^{56} - 416 q^{57} - 1072 q^{58} - 420 q^{59} - 712 q^{60} - 224 q^{61} - 448 q^{62} - 244 q^{63} - 272 q^{64} - 424 q^{65} - 536 q^{66} + 152 q^{67} - 512 q^{68} - 712 q^{69} - 648 q^{70} + 240 q^{71} - 200 q^{72} - 380 q^{73} + 168 q^{74} + 52 q^{75} + 616 q^{76} - 520 q^{77} + 152 q^{78} + 1008 q^{79} - 168 q^{80} + 642 q^{81} - 808 q^{82} + 1432 q^{83} - 480 q^{84} + 392 q^{85} - 512 q^{86} + 1376 q^{87} + 224 q^{88} + 452 q^{89} + 1752 q^{90} + 752 q^{91} + 624 q^{92} + 752 q^{93} + 1584 q^{94} + 472 q^{95} + 2400 q^{96} + 796 q^{97} + 1552 q^{98} + 68 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(160))\)

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
160.3.b \(\chi_{160}(31, \cdot)\) 160.3.b.a 4 1
160.3.b.b 4
160.3.e \(\chi_{160}(79, \cdot)\) 160.3.e.a 1 1
160.3.e.b 1
160.3.e.c 8
160.3.g \(\chi_{160}(111, \cdot)\) 160.3.g.a 8 1
160.3.h \(\chi_{160}(159, \cdot)\) 160.3.h.a 6 1
160.3.h.b 6
160.3.i \(\chi_{160}(57, \cdot)\) None 0 2
160.3.k \(\chi_{160}(39, \cdot)\) None 0 2
160.3.m \(\chi_{160}(17, \cdot)\) 160.3.m.a 20 2
160.3.p \(\chi_{160}(33, \cdot)\) 160.3.p.a 2 2
160.3.p.b 2
160.3.p.c 4
160.3.p.d 4
160.3.p.e 6
160.3.p.f 6
160.3.r \(\chi_{160}(71, \cdot)\) None 0 2
160.3.t \(\chi_{160}(137, \cdot)\) None 0 2
160.3.v \(\chi_{160}(13, \cdot)\) 160.3.v.a 184 4
160.3.w \(\chi_{160}(11, \cdot)\) 160.3.w.a 128 4
160.3.y \(\chi_{160}(19, \cdot)\) 160.3.y.a 184 4
160.3.bb \(\chi_{160}(53, \cdot)\) 160.3.bb.a 184 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(160))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(160)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)