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Properties

Label 160.6
Level 160
Weight 6
Dimension 1950
Nonzero newspaces 10
Sturm bound 9216
Trace bound 7

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Defining parameters

Level: \( N \) = \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 10 \)
Sturm bound: \(9216\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(160))\).

Total New Old
Modular forms 3968 2010 1958
Cusp forms 3712 1950 1762
Eisenstein series 256 60 196

Trace form

\( 1950 q - 8 q^{2} - 4 q^{3} - 8 q^{4} - 50 q^{5} - 24 q^{6} + 188 q^{7} - 8 q^{8} - 586 q^{9} + O(q^{10}) \) \( 1950 q - 8 q^{2} - 4 q^{3} - 8 q^{4} - 50 q^{5} - 24 q^{6} + 188 q^{7} - 8 q^{8} - 586 q^{9} + 188 q^{10} - 16 q^{11} + 3160 q^{12} - 228 q^{13} - 4968 q^{14} - 428 q^{15} - 8384 q^{16} - 3628 q^{17} + 3232 q^{18} - 8 q^{19} + 7588 q^{20} + 11752 q^{21} + 24752 q^{22} + 1324 q^{23} - 42928 q^{24} + 5826 q^{25} - 25984 q^{26} + 13952 q^{27} + 4352 q^{28} - 24492 q^{29} + 32300 q^{30} - 57672 q^{31} + 37152 q^{32} + 16040 q^{33} + 12496 q^{34} + 9544 q^{35} - 131200 q^{36} - 23132 q^{37} - 824 q^{38} + 111344 q^{39} + 28936 q^{40} + 32068 q^{41} + 107232 q^{42} - 65460 q^{43} - 7448 q^{44} - 2638 q^{45} - 126680 q^{46} - 44196 q^{47} - 224752 q^{48} - 61674 q^{49} + 4508 q^{50} + 18920 q^{51} - 36952 q^{52} + 171396 q^{53} - 2640 q^{54} - 37084 q^{55} + 161936 q^{56} + 271976 q^{57} + 169136 q^{58} + 57912 q^{59} + 62456 q^{60} - 409364 q^{61} - 126976 q^{62} + 76900 q^{63} + 651376 q^{64} + 47484 q^{65} + 220232 q^{66} + 33060 q^{67} - 304512 q^{68} - 27752 q^{69} - 742776 q^{70} - 18160 q^{71} - 773960 q^{72} + 80092 q^{73} - 329240 q^{74} - 65520 q^{75} - 24984 q^{76} + 121144 q^{77} + 1611672 q^{78} - 246096 q^{79} + 1082840 q^{80} + 117998 q^{81} - 135848 q^{82} + 784916 q^{83} - 775136 q^{84} + 55348 q^{85} - 903968 q^{86} + 896952 q^{87} - 846240 q^{88} - 43204 q^{89} - 1676136 q^{90} - 729680 q^{91} - 84496 q^{92} - 1034640 q^{93} + 76400 q^{94} - 811424 q^{95} + 2219360 q^{96} + 123076 q^{97} + 2413200 q^{98} - 677104 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(160))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
160.6.a \(\chi_{160}(1, \cdot)\) 160.6.a.a 2 1
160.6.a.b 2
160.6.a.c 2
160.6.a.d 2
160.6.a.e 2
160.6.a.f 3
160.6.a.g 3
160.6.a.h 4
160.6.c \(\chi_{160}(129, \cdot)\) 160.6.c.a 2 1
160.6.c.b 4
160.6.c.c 12
160.6.c.d 12
160.6.d \(\chi_{160}(81, \cdot)\) 160.6.d.a 20 1
160.6.f \(\chi_{160}(49, \cdot)\) 160.6.f.a 28 1
160.6.j \(\chi_{160}(87, \cdot)\) None 0 2
160.6.l \(\chi_{160}(41, \cdot)\) None 0 2
160.6.n \(\chi_{160}(63, \cdot)\) 160.6.n.a 14 2
160.6.n.b 14
160.6.n.c 16
160.6.n.d 16
160.6.o \(\chi_{160}(47, \cdot)\) 160.6.o.a 56 2
160.6.q \(\chi_{160}(9, \cdot)\) None 0 2
160.6.s \(\chi_{160}(7, \cdot)\) None 0 2
160.6.u \(\chi_{160}(43, \cdot)\) n/a 472 4
160.6.x \(\chi_{160}(21, \cdot)\) n/a 320 4
160.6.z \(\chi_{160}(29, \cdot)\) n/a 472 4
160.6.ba \(\chi_{160}(3, \cdot)\) n/a 472 4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(160))\) into lower level spaces

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