Properties

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

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Defining parameters

Level: \( N \) = \( 167 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 3 \)
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

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

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