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Properties

Label 161.8
Level 161
Weight 8
Dimension 6952
Nonzero newspaces 8
Sturm bound 16896
Trace bound 2

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Defining parameters

Level: \( N \) = \( 161 = 7 \cdot 23 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(16896\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(161))\).

Total New Old
Modular forms 7524 7164 360
Cusp forms 7260 6952 308
Eisenstein series 264 212 52

Trace form

\( 6952 q - 38 q^{2} - 92 q^{3} + 474 q^{4} - 32 q^{5} - 2624 q^{6} - 713 q^{7} + 3556 q^{8} + 1270 q^{9} + O(q^{10}) \) \( 6952 q - 38 q^{2} - 92 q^{3} + 474 q^{4} - 32 q^{5} - 2624 q^{6} - 713 q^{7} + 3556 q^{8} + 1270 q^{9} + 18136 q^{10} - 2540 q^{11} - 40784 q^{12} + 9896 q^{13} - 93001 q^{14} + 18416 q^{15} - 78158 q^{16} + 164246 q^{17} + 647870 q^{18} + 31810 q^{19} - 745036 q^{20} - 505534 q^{21} - 15408 q^{22} - 171156 q^{23} + 699284 q^{24} + 507238 q^{25} + 208092 q^{26} + 324286 q^{27} - 621121 q^{28} - 428716 q^{29} - 944200 q^{30} + 223690 q^{31} - 1603674 q^{32} + 1944098 q^{33} + 3411372 q^{34} - 1070109 q^{35} - 6743834 q^{36} - 2283312 q^{37} + 3507774 q^{38} + 7141996 q^{39} + 11165940 q^{40} - 151428 q^{41} + 156239 q^{42} - 2269806 q^{43} - 15530354 q^{44} - 16730518 q^{45} - 14094522 q^{46} + 1360104 q^{47} + 10619016 q^{48} + 8460337 q^{49} + 13087550 q^{50} + 7744900 q^{51} + 22849128 q^{52} - 2198820 q^{53} + 20034960 q^{54} - 3103832 q^{55} - 20691822 q^{56} - 51964244 q^{57} - 44636270 q^{58} + 8214952 q^{59} + 79663976 q^{60} + 32563944 q^{61} + 46130212 q^{62} + 23355234 q^{63} + 14360624 q^{64} - 14909050 q^{65} - 44445750 q^{66} - 16806560 q^{67} - 81247834 q^{68} - 46428006 q^{69} - 47306722 q^{70} - 14029272 q^{71} + 16612936 q^{72} + 17157340 q^{73} + 142031422 q^{74} + 114343590 q^{75} + 26378582 q^{76} + 7299908 q^{77} - 67254874 q^{78} - 526900 q^{79} - 21733462 q^{80} + 16358438 q^{81} - 62030812 q^{82} - 65686882 q^{83} - 13369737 q^{84} + 89054666 q^{85} + 201579016 q^{86} + 43122364 q^{87} - 46829820 q^{88} - 67224692 q^{89} - 260006438 q^{90} - 56212256 q^{91} - 113194904 q^{92} - 89270200 q^{93} - 43508238 q^{94} + 64619290 q^{95} + 78163554 q^{96} - 40286698 q^{97} - 176427780 q^{98} + 64773208 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(161))\)

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
161.8.a \(\chi_{161}(1, \cdot)\) 161.8.a.a 16 1
161.8.a.b 19
161.8.a.c 20
161.8.a.d 23
161.8.c \(\chi_{161}(160, \cdot)\) n/a 110 1
161.8.e \(\chi_{161}(93, \cdot)\) n/a 204 2
161.8.g \(\chi_{161}(45, \cdot)\) n/a 220 2
161.8.i \(\chi_{161}(8, \cdot)\) n/a 840 10
161.8.k \(\chi_{161}(20, \cdot)\) n/a 1100 10
161.8.m \(\chi_{161}(2, \cdot)\) n/a 2200 20
161.8.o \(\chi_{161}(5, \cdot)\) n/a 2200 20

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(161))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(161)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 1}\)