Properties

Label 167.1
Level 167
Weight 1
Dimension 5
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 2324
Trace bound 0

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Defining parameters

Level: \( N \) = \( 167 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(2324\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(167))\).

Total New Old
Modular forms 88 88 0
Cusp forms 5 5 0
Eisenstein series 83 83 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 5 0 0 0

Trace form

\( 5 q - q^{2} - q^{3} + 4 q^{4} - 2 q^{6} - q^{7} - 2 q^{8} + 4 q^{9} + O(q^{10}) \) \( 5 q - q^{2} - q^{3} + 4 q^{4} - 2 q^{6} - q^{7} - 2 q^{8} + 4 q^{9} - q^{11} - 3 q^{12} - 2 q^{14} + 3 q^{16} - 3 q^{18} - q^{19} - 2 q^{21} - 2 q^{22} - 4 q^{24} + 5 q^{25} - 2 q^{27} - 3 q^{28} - q^{29} - q^{31} - 3 q^{32} - 2 q^{33} + q^{36} - 2 q^{38} + 7 q^{42} + 8 q^{44} - q^{47} + 6 q^{48} + 4 q^{49} - q^{50} + 7 q^{54} - 4 q^{56} - 2 q^{57} - 2 q^{58} - q^{61} + 9 q^{62} - 3 q^{63} + 2 q^{64} - 4 q^{66} + 5 q^{72} - q^{75} - 3 q^{76} - 2 q^{77} + 3 q^{81} + 5 q^{84} - 2 q^{87} - 4 q^{88} - q^{89} - 2 q^{93} - 2 q^{94} - 6 q^{96} - q^{97} + 8 q^{98} - 3 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(167))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
167.1.b \(\chi_{167}(166, \cdot)\) 167.1.b.a 5 1
167.1.d \(\chi_{167}(5, \cdot)\) None 0 82