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Properties

Label 2339.1
Level 2339
Weight 1
Dimension 9
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 455910
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2339 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(455910\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2339))\).

Total New Old
Modular forms 1178 1178 0
Cusp forms 9 9 0
Eisenstein series 1169 1169 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 9 0 0 0

Trace form

\( 9 q - q^{3} + 9 q^{4} - q^{5} + 8 q^{9} + O(q^{10}) \) \( 9 q - q^{3} + 9 q^{4} - q^{5} + 8 q^{9} - q^{11} - q^{12} - q^{13} - 2 q^{15} + 9 q^{16} - q^{19} - q^{20} + 8 q^{25} - 2 q^{27} - 2 q^{33} + 8 q^{36} - 2 q^{39} - q^{41} - q^{44} - 3 q^{45} - q^{48} + 9 q^{49} - q^{52} - q^{53} - 2 q^{55} - 2 q^{57} - q^{59} - 2 q^{60} + 9 q^{64} - 2 q^{65} - q^{67} - q^{71} - q^{73} - 3 q^{75} - q^{76} - q^{79} - q^{80} + 7 q^{81} - q^{83} - q^{89} - 2 q^{95} - q^{97} - 3 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2339))\)

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
2339.1.b \(\chi_{2339}(2338, \cdot)\) 2339.1.b.a 9 1
2339.1.d \(\chi_{2339}(190, \cdot)\) None 0 6
2339.1.f \(\chi_{2339}(6, \cdot)\) None 0 166
2339.1.h \(\chi_{2339}(2, \cdot)\) None 0 996