Properties

Label 167.2
Level 167
Weight 2
Dimension 1080
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 4648
Trace bound 1

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Defining parameters

Level: \( N \) = \( 167 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(4648\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(167))\).

Total New Old
Modular forms 1245 1245 0
Cusp forms 1080 1080 0
Eisenstein series 165 165 0

Trace form

\( 1080 q - 80 q^{2} - 79 q^{3} - 76 q^{4} - 77 q^{5} - 71 q^{6} - 75 q^{7} - 68 q^{8} - 70 q^{9} + O(q^{10}) \) \( 1080 q - 80 q^{2} - 79 q^{3} - 76 q^{4} - 77 q^{5} - 71 q^{6} - 75 q^{7} - 68 q^{8} - 70 q^{9} - 65 q^{10} - 71 q^{11} - 55 q^{12} - 69 q^{13} - 59 q^{14} - 59 q^{15} - 52 q^{16} - 65 q^{17} - 44 q^{18} - 63 q^{19} - 41 q^{20} - 51 q^{21} - 47 q^{22} - 59 q^{23} - 23 q^{24} - 52 q^{25} - 41 q^{26} - 43 q^{27} - 27 q^{28} - 53 q^{29} - 11 q^{30} - 51 q^{31} - 20 q^{32} - 35 q^{33} - 29 q^{34} - 35 q^{35} + 8 q^{36} - 45 q^{37} - 23 q^{38} - 27 q^{39} + 7 q^{40} - 41 q^{41} + 13 q^{42} - 39 q^{43} + q^{44} - 5 q^{45} - 11 q^{46} - 35 q^{47} + 41 q^{48} - 26 q^{49} + 10 q^{50} - 11 q^{51} + 15 q^{52} - 29 q^{53} + 37 q^{54} - 11 q^{55} + 37 q^{56} - 3 q^{57} + 7 q^{58} - 23 q^{59} + 85 q^{60} - 21 q^{61} + 13 q^{62} + 21 q^{63} + 44 q^{64} + q^{65} + 61 q^{66} - 15 q^{67} + 43 q^{68} + 13 q^{69} + 61 q^{70} - 11 q^{71} + 112 q^{72} - 9 q^{73} + 31 q^{74} + 41 q^{75} + 57 q^{76} + 13 q^{77} + 85 q^{78} - 3 q^{79} + 103 q^{80} + 38 q^{81} + 43 q^{82} + q^{83} + 141 q^{84} + 25 q^{85} + 49 q^{86} + 37 q^{87} + 97 q^{88} + 7 q^{89} + 151 q^{90} + 29 q^{91} + 85 q^{92} + 45 q^{93} + 61 q^{94} + 37 q^{95} + 169 q^{96} + 15 q^{97} + 88 q^{98} + 73 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
167.2.a \(\chi_{167}(1, \cdot)\) 167.2.a.a 2 1
167.2.a.b 12
167.2.c \(\chi_{167}(2, \cdot)\) 167.2.c.a 1066 82