Properties

Label 160.4
Level 160
Weight 4
Dimension 1158
Nonzero newspaces 10
Newform subspaces 24
Sturm bound 6144
Trace bound 7

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Defining parameters

Level: \( N \) = \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 24 \)
Sturm bound: \(6144\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(160))\).

Total New Old
Modular forms 2432 1218 1214
Cusp forms 2176 1158 1018
Eisenstein series 256 60 196

Trace form

\( 1158q - 8q^{2} - 4q^{3} - 8q^{4} - 14q^{5} - 24q^{6} - 36q^{7} - 8q^{8} - 106q^{9} + O(q^{10}) \) \( 1158q - 8q^{2} - 4q^{3} - 8q^{4} - 14q^{5} - 24q^{6} - 36q^{7} - 8q^{8} - 106q^{9} - 132q^{10} - 16q^{11} + 88q^{12} + 228q^{13} + 408q^{14} + 100q^{15} + 576q^{16} + 356q^{17} + 352q^{18} - 8q^{19} - 92q^{20} - 536q^{21} - 400q^{22} - 1268q^{23} + 80q^{24} - 230q^{25} - 64q^{26} + 416q^{27} - 768q^{28} - 180q^{29} - 1204q^{30} + 1848q^{31} - 1248q^{32} + 824q^{33} - 1072q^{34} + 904q^{35} - 2944q^{36} - 356q^{37} - 1976q^{38} - 1072q^{39} + 520q^{40} + 244q^{41} + 4512q^{42} - 756q^{43} + 4072q^{44} + 1574q^{45} + 2856q^{46} + 924q^{47} + 4880q^{48} + 510q^{49} + 3548q^{50} + 1256q^{51} + 5032q^{52} - 2052q^{53} + 2160q^{54} - 556q^{55} - 2416q^{56} - 1864q^{57} - 6416q^{58} - 2760q^{59} - 4744q^{60} + 1844q^{61} - 6784q^{62} - 3740q^{63} - 2192q^{64} + 2436q^{65} + 1160q^{66} - 2236q^{67} + 384q^{68} + 3544q^{69} + 168q^{70} - 976q^{71} - 2120q^{72} - 884q^{73} - 1688q^{74} - 1104q^{75} + 1640q^{76} - 8264q^{77} + 408q^{78} - 5008q^{79} - 2344q^{80} - 6874q^{81} + 1112q^{82} - 7564q^{83} - 4832q^{84} - 3748q^{85} - 2912q^{86} + 4536q^{87} - 3744q^{88} + 4268q^{89} + 24q^{90} + 8880q^{91} - 9232q^{92} - 144q^{93} - 11024q^{94} + 8656q^{95} - 10912q^{96} + 2516q^{97} - 9840q^{98} + 10832q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(160))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
160.4.a \(\chi_{160}(1, \cdot)\) 160.4.a.a 1 1
160.4.a.b 1
160.4.a.c 2
160.4.a.d 2
160.4.a.e 2
160.4.a.f 2
160.4.a.g 2
160.4.c \(\chi_{160}(129, \cdot)\) 160.4.c.a 2 1
160.4.c.b 4
160.4.c.c 4
160.4.c.d 8
160.4.d \(\chi_{160}(81, \cdot)\) 160.4.d.a 12 1
160.4.f \(\chi_{160}(49, \cdot)\) 160.4.f.a 16 1
160.4.j \(\chi_{160}(87, \cdot)\) None 0 2
160.4.l \(\chi_{160}(41, \cdot)\) None 0 2
160.4.n \(\chi_{160}(63, \cdot)\) 160.4.n.a 2 2
160.4.n.b 2
160.4.n.c 8
160.4.n.d 8
160.4.n.e 8
160.4.n.f 8
160.4.o \(\chi_{160}(47, \cdot)\) 160.4.o.a 32 2
160.4.q \(\chi_{160}(9, \cdot)\) None 0 2
160.4.s \(\chi_{160}(7, \cdot)\) None 0 2
160.4.u \(\chi_{160}(43, \cdot)\) 160.4.u.a 280 4
160.4.x \(\chi_{160}(21, \cdot)\) 160.4.x.a 192 4
160.4.z \(\chi_{160}(29, \cdot)\) 160.4.z.a 280 4
160.4.ba \(\chi_{160}(3, \cdot)\) 160.4.ba.a 280 4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(160))\) into lower level spaces

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