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Properties

Label 139.1
Level 139
Weight 1
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 1610
Trace bound 0

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Defining parameters

Level: \( N \) = \( 139 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(1610\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(139))\).

Total New Old
Modular forms 70 70 0
Cusp forms 1 1 0
Eisenstein series 69 69 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

\( q + q^{4} - q^{5} - q^{7} + q^{9} + O(q^{10}) \) \( q + q^{4} - q^{5} - q^{7} + q^{9} - q^{11} - q^{13} + q^{16} - q^{20} - q^{28} - q^{29} - q^{31} + q^{35} + q^{36} + 2 q^{37} + 2 q^{41} - q^{44} - q^{45} + 2 q^{47} - q^{52} + q^{55} - q^{63} + q^{64} + q^{65} - q^{67} - q^{71} + q^{77} - q^{79} - q^{80} + q^{81} - q^{83} - q^{89} + q^{91} - q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(139))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
139.1.b \(\chi_{139}(138, \cdot)\) 139.1.b.a 1 1
139.1.d \(\chi_{139}(43, \cdot)\) None 0 2
139.1.f \(\chi_{139}(8, \cdot)\) None 0 22
139.1.h \(\chi_{139}(2, \cdot)\) None 0 44