Properties

Label 1931.1
Level 1931
Weight 1
Dimension 12
Nonzero newspaces 1
Newform subspaces 4
Sturm bound 310730
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1931 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 4 \)
Sturm bound: \(310730\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1931))\).

Total New Old
Modular forms 977 977 0
Cusp forms 12 12 0
Eisenstein series 965 965 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 10 0 2 0

Trace form

\( 12 q - q^{3} + 8 q^{4} - 3 q^{5} + q^{7} + 7 q^{9} + O(q^{10}) \) \( 12 q - q^{3} + 8 q^{4} - 3 q^{5} + q^{7} + 7 q^{9} + q^{11} - q^{12} - 2 q^{15} + 8 q^{16} - q^{19} + q^{20} - 2 q^{21} - 3 q^{23} + 9 q^{25} - 2 q^{27} - 3 q^{28} - 2 q^{33} - 4 q^{34} - 4 q^{35} + 11 q^{36} + q^{37} + q^{41} - 3 q^{43} - 3 q^{44} - q^{45} - q^{48} + 9 q^{49} - 4 q^{55} - 2 q^{57} - 4 q^{58} - 3 q^{59} - 2 q^{60} - 4 q^{62} - 5 q^{63} + 12 q^{64} - 2 q^{69} - q^{71} - 3 q^{75} - q^{76} + q^{79} + q^{80} + 10 q^{81} + q^{83} - 2 q^{84} + q^{92} - 2 q^{95} - 3 q^{97} - 5 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1931))\)

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
1931.1.b \(\chi_{1931}(1930, \cdot)\) 1931.1.b.a 1 1
1931.1.b.b 2
1931.1.b.c 3
1931.1.b.d 6
1931.1.d \(\chi_{1931}(114, \cdot)\) None 0 4
1931.1.f \(\chi_{1931}(6, \cdot)\) None 0 192
1931.1.h \(\chi_{1931}(2, \cdot)\) None 0 768