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Properties

Label 131.1
Level 131
Weight 1
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 1430
Trace bound 0

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Defining parameters

Level: \( N \) = \( 131 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(1430\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(131))\).

Total New Old
Modular forms 67 67 0
Cusp forms 2 2 0
Eisenstein series 65 65 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q - q^{3} + 2 q^{4} - q^{5} - q^{7} + q^{9} + O(q^{10}) \) \( 2 q - q^{3} + 2 q^{4} - q^{5} - q^{7} + q^{9} - q^{11} - q^{12} - q^{13} - 2 q^{15} + 2 q^{16} - q^{20} - 2 q^{21} + q^{25} - 2 q^{27} - q^{28} + 3 q^{33} + 3 q^{35} + q^{36} + 3 q^{39} - q^{41} - q^{43} - q^{44} + 2 q^{45} - q^{48} + q^{49} - q^{52} + 4 q^{53} - 2 q^{55} - q^{59} - 2 q^{60} - q^{61} + 2 q^{63} + 2 q^{64} - 2 q^{65} + 2 q^{75} - 2 q^{77} - q^{80} - 2 q^{84} + 4 q^{89} - 2 q^{91} - 3 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(131))\)

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
131.1.b \(\chi_{131}(130, \cdot)\) 131.1.b.a 2 1
131.1.d \(\chi_{131}(42, \cdot)\) None 0 4
131.1.f \(\chi_{131}(18, \cdot)\) None 0 12
131.1.h \(\chi_{131}(2, \cdot)\) None 0 48