Properties

Label 107.1
Level 107
Weight 1
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 954
Trace bound 0

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Defining parameters

Level: \( N \) = \( 107 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(954\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(107))\).

Total New Old
Modular forms 54 54 0
Cusp forms 1 1 0
Eisenstein series 53 53 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\( q - q^{3} + q^{4} + O(q^{10}) \) \( q - q^{3} + q^{4} - q^{11} - q^{12} - q^{13} + q^{16} - q^{19} - q^{23} + q^{25} + q^{27} + 2 q^{29} + q^{33} - q^{37} + q^{39} - q^{41} - q^{44} + 2 q^{47} - q^{48} + q^{49} - q^{52} - q^{53} + q^{57} - q^{61} + q^{64} + q^{69} - q^{75} - q^{76} - q^{79} - q^{81} + 2 q^{83} - 2 q^{87} - q^{89} - q^{92} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(107))\)

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
107.1.b \(\chi_{107}(106, \cdot)\) 107.1.b.a 1 1
107.1.d \(\chi_{107}(2, \cdot)\) None 0 52