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Properties

Label 161.3
Level 161
Weight 3
Dimension 1912
Nonzero newspaces 8
Newform subspaces 9
Sturm bound 6336
Trace bound 2

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Defining parameters

Level: \( N \) = \( 161 = 7 \cdot 23 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 9 \)
Sturm bound: \(6336\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(161))\).

Total New Old
Modular forms 2244 2120 124
Cusp forms 1980 1912 68
Eisenstein series 264 208 56

Trace form

\( 1912 q - 38 q^{2} - 44 q^{3} - 54 q^{4} - 44 q^{5} - 44 q^{6} - 41 q^{7} - 104 q^{8} - 62 q^{9} + O(q^{10}) \) \( 1912 q - 38 q^{2} - 44 q^{3} - 54 q^{4} - 44 q^{5} - 44 q^{6} - 41 q^{7} - 104 q^{8} - 62 q^{9} - 44 q^{10} - 32 q^{11} - 44 q^{12} - 44 q^{13} - 97 q^{14} - 264 q^{15} - 286 q^{16} - 154 q^{17} - 342 q^{18} - 110 q^{19} - 220 q^{20} - 88 q^{21} - 168 q^{22} - 18 q^{23} + 176 q^{24} + 38 q^{25} + 132 q^{26} + 286 q^{27} + 279 q^{28} + 152 q^{29} + 660 q^{30} + 154 q^{31} + 306 q^{32} + 198 q^{33} - 528 q^{34} - 275 q^{35} - 1190 q^{36} - 672 q^{37} - 814 q^{38} - 572 q^{39} - 924 q^{40} - 220 q^{41} - 385 q^{42} - 402 q^{43} - 226 q^{44} - 66 q^{45} + 186 q^{46} + 88 q^{47} + 572 q^{48} + 111 q^{49} + 810 q^{50} + 484 q^{51} + 1496 q^{52} + 320 q^{53} + 924 q^{54} + 264 q^{55} - 284 q^{56} + 220 q^{57} + 182 q^{58} - 220 q^{59} - 1144 q^{60} - 660 q^{61} - 836 q^{62} - 204 q^{63} - 632 q^{64} - 506 q^{65} - 594 q^{66} + 148 q^{67} - 66 q^{68} + 66 q^{69} + 66 q^{70} - 8 q^{71} + 1264 q^{72} + 176 q^{73} + 410 q^{74} - 374 q^{75} - 286 q^{76} - 260 q^{77} - 1650 q^{78} + 56 q^{79} + 418 q^{80} - 1702 q^{81} + 242 q^{83} - 77 q^{84} - 682 q^{85} - 4 q^{86} - 1100 q^{87} - 960 q^{88} - 308 q^{89} - 550 q^{90} - 66 q^{91} - 2 q^{92} + 440 q^{93} + 638 q^{94} + 242 q^{95} + 814 q^{96} - 374 q^{97} - 388 q^{98} + 460 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(161))\)

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
161.3.b \(\chi_{161}(139, \cdot)\) 161.3.b.a 28 1
161.3.d \(\chi_{161}(22, \cdot)\) 161.3.d.a 24 1
161.3.f \(\chi_{161}(114, \cdot)\) 161.3.f.a 60 2
161.3.h \(\chi_{161}(24, \cdot)\) 161.3.h.a 60 2
161.3.j \(\chi_{161}(15, \cdot)\) 161.3.j.a 240 10
161.3.l \(\chi_{161}(6, \cdot)\) 161.3.l.a 20 10
161.3.l.b 280
161.3.n \(\chi_{161}(3, \cdot)\) 161.3.n.a 600 20
161.3.p \(\chi_{161}(11, \cdot)\) 161.3.p.a 600 20

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(161))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(161)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)