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Properties

Label 163.2
Level 163
Weight 2
Dimension 1027
Nonzero newspaces 5
Newform subspaces 7
Sturm bound 4428
Trace bound 1

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Defining parameters

Level: \( N \) = \( 163 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 7 \)
Sturm bound: \(4428\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(163))\).

Total New Old
Modular forms 1188 1188 0
Cusp forms 1027 1027 0
Eisenstein series 161 161 0

Trace form

\( 1027 q - 78 q^{2} - 77 q^{3} - 74 q^{4} - 75 q^{5} - 69 q^{6} - 73 q^{7} - 66 q^{8} - 68 q^{9} + O(q^{10}) \) \( 1027 q - 78 q^{2} - 77 q^{3} - 74 q^{4} - 75 q^{5} - 69 q^{6} - 73 q^{7} - 66 q^{8} - 68 q^{9} - 63 q^{10} - 69 q^{11} - 53 q^{12} - 67 q^{13} - 57 q^{14} - 57 q^{15} - 50 q^{16} - 63 q^{17} - 42 q^{18} - 61 q^{19} - 39 q^{20} - 49 q^{21} - 45 q^{22} - 57 q^{23} - 21 q^{24} - 50 q^{25} - 39 q^{26} - 41 q^{27} - 25 q^{28} - 51 q^{29} - 9 q^{30} - 49 q^{31} - 18 q^{32} - 33 q^{33} - 27 q^{34} - 33 q^{35} + 10 q^{36} - 43 q^{37} - 21 q^{38} - 25 q^{39} + 9 q^{40} - 39 q^{41} + 15 q^{42} - 37 q^{43} + 3 q^{44} - 3 q^{45} - 9 q^{46} - 33 q^{47} + 43 q^{48} - 24 q^{49} + 12 q^{50} - 9 q^{51} + 17 q^{52} - 27 q^{53} + 39 q^{54} - 9 q^{55} + 39 q^{56} - q^{57} + 9 q^{58} - 21 q^{59} + 87 q^{60} - 19 q^{61} + 15 q^{62} + 23 q^{63} + 46 q^{64} + 3 q^{65} + 63 q^{66} - 13 q^{67} + 45 q^{68} + 15 q^{69} + 63 q^{70} - 9 q^{71} + 114 q^{72} - 7 q^{73} + 33 q^{74} + 43 q^{75} + 59 q^{76} + 15 q^{77} + 87 q^{78} - q^{79} + 105 q^{80} + 40 q^{81} + 45 q^{82} + 3 q^{83} + 143 q^{84} + 27 q^{85} + 51 q^{86} + 39 q^{87} + 99 q^{88} + 9 q^{89} + 153 q^{90} + 31 q^{91} + 87 q^{92} + 47 q^{93} + 63 q^{94} + 39 q^{95} + 171 q^{96} + 17 q^{97} + 90 q^{98} + 75 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(163))\)

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
163.2.a \(\chi_{163}(1, \cdot)\) 163.2.a.a 1 1
163.2.a.b 5
163.2.a.c 7
163.2.c \(\chi_{163}(58, \cdot)\) 163.2.c.a 24 2
163.2.e \(\chi_{163}(38, \cdot)\) 163.2.e.a 72 6
163.2.g \(\chi_{163}(6, \cdot)\) 163.2.g.a 216 18
163.2.i \(\chi_{163}(4, \cdot)\) 163.2.i.a 702 54