Properties

Label 983.1
Level 983
Weight 1
Dimension 13
Nonzero newspaces 1
Newform subspaces 3
Sturm bound 80524
Trace bound 0

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Defining parameters

Level: \( N \) = \( 983 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 3 \)
Sturm bound: \(80524\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(983))\).

Total New Old
Modular forms 504 504 0
Cusp forms 13 13 0
Eisenstein series 491 491 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 13 0 0 0

Trace form

\( 13 q - q^{2} - q^{3} + 12 q^{4} - 2 q^{6} - q^{7} - 2 q^{8} + 12 q^{9} + O(q^{10}) \) \( 13 q - q^{2} - q^{3} + 12 q^{4} - 2 q^{6} - q^{7} - 2 q^{8} + 12 q^{9} - 3 q^{12} - 2 q^{14} + 11 q^{16} - 3 q^{18} - q^{19} - 2 q^{21} - q^{23} - 4 q^{24} + 13 q^{25} - 2 q^{27} - 3 q^{28} - q^{31} - 3 q^{32} + 9 q^{36} - q^{37} - 2 q^{38} - q^{41} - 4 q^{42} - q^{43} - 2 q^{46} - q^{47} - 5 q^{48} + 12 q^{49} - q^{50} - q^{53} - 4 q^{54} - 4 q^{56} - 2 q^{57} - q^{59} - 2 q^{62} - 3 q^{63} + 10 q^{64} - q^{67} - 2 q^{69} - 6 q^{72} - 2 q^{74} - q^{75} - 3 q^{76} - q^{79} + 11 q^{81} - 2 q^{82} - 6 q^{84} - 2 q^{86} - q^{89} - 3 q^{92} - 2 q^{93} - 2 q^{94} - 6 q^{96} - 3 q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(983))\)

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
983.1.b \(\chi_{983}(982, \cdot)\) 983.1.b.a 1 1
983.1.b.b 3
983.1.b.c 9
983.1.d \(\chi_{983}(5, \cdot)\) None 0 490