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Properties

Label 163.3
Level 163
Weight 3
Dimension 2133
Nonzero newspaces 5
Newform subspaces 6
Sturm bound 6642
Trace bound 1

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Defining parameters

Level: \( N \) = \( 163 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 6 \)
Sturm bound: \(6642\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(163))\).

Total New Old
Modular forms 2295 2295 0
Cusp forms 2133 2133 0
Eisenstein series 162 162 0

Trace form

\( 2133 q - 81 q^{2} - 81 q^{3} - 81 q^{4} - 81 q^{5} - 81 q^{6} - 81 q^{7} - 81 q^{8} - 81 q^{9} + O(q^{10}) \) \( 2133 q - 81 q^{2} - 81 q^{3} - 81 q^{4} - 81 q^{5} - 81 q^{6} - 81 q^{7} - 81 q^{8} - 81 q^{9} - 81 q^{10} - 81 q^{11} - 81 q^{12} - 81 q^{13} - 81 q^{14} - 81 q^{15} - 81 q^{16} - 81 q^{17} - 81 q^{18} - 81 q^{19} - 81 q^{20} - 81 q^{21} - 81 q^{22} - 81 q^{23} - 81 q^{24} - 81 q^{25} - 81 q^{26} - 81 q^{27} - 81 q^{28} - 81 q^{29} - 81 q^{30} - 81 q^{31} - 81 q^{32} - 81 q^{33} - 81 q^{34} - 81 q^{35} - 81 q^{36} - 81 q^{37} - 81 q^{38} - 81 q^{39} - 81 q^{40} - 81 q^{41} - 81 q^{42} - 81 q^{43} - 81 q^{44} - 81 q^{45} - 81 q^{46} - 81 q^{47} - 81 q^{48} - 81 q^{49} - 81 q^{50} - 81 q^{51} - 81 q^{52} - 81 q^{53} - 81 q^{54} - 81 q^{55} - 81 q^{56} - 81 q^{57} - 81 q^{58} - 81 q^{59} - 81 q^{60} - 81 q^{61} - 81 q^{62} - 81 q^{63} - 81 q^{64} - 81 q^{65} - 81 q^{66} - 81 q^{67} - 81 q^{68} - 81 q^{69} - 81 q^{70} - 81 q^{71} - 81 q^{72} - 81 q^{73} - 81 q^{74} - 81 q^{75} - 81 q^{76} - 81 q^{77} - 81 q^{78} - 81 q^{79} - 81 q^{80} - 81 q^{81} - 81 q^{82} - 81 q^{83} - 81 q^{84} - 81 q^{85} - 81 q^{86} - 81 q^{87} - 81 q^{88} - 81 q^{89} - 81 q^{90} - 81 q^{91} - 81 q^{92} - 81 q^{93} - 81 q^{94} - 81 q^{95} - 81 q^{96} - 81 q^{97} - 81 q^{98} - 81 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(163))\)

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
163.3.b \(\chi_{163}(162, \cdot)\) 163.3.b.a 1 1
163.3.b.b 26
163.3.d \(\chi_{163}(59, \cdot)\) 163.3.d.a 54 2
163.3.f \(\chi_{163}(23, \cdot)\) 163.3.f.a 162 6
163.3.h \(\chi_{163}(5, \cdot)\) 163.3.h.a 486 18
163.3.j \(\chi_{163}(2, \cdot)\) 163.3.j.a 1404 54