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Properties

Label 983.4
Level 983
Weight 4
Dimension 120295
Nonzero newspaces 2
Sturm bound 322096
Trace bound 1

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Defining parameters

Level: \( N \) = \( 983 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 2 \)
Sturm bound: \(322096\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(983))\).

Total New Old
Modular forms 121277 121275 2
Cusp forms 120295 120295 0
Eisenstein series 982 980 2

Trace form

\( 120295 q - 491 q^{2} - 491 q^{3} - 491 q^{4} - 491 q^{5} - 491 q^{6} - 491 q^{7} - 491 q^{8} - 491 q^{9} + O(q^{10}) \) \( 120295 q - 491 q^{2} - 491 q^{3} - 491 q^{4} - 491 q^{5} - 491 q^{6} - 491 q^{7} - 491 q^{8} - 491 q^{9} - 491 q^{10} - 491 q^{11} - 491 q^{12} - 491 q^{13} - 491 q^{14} - 491 q^{15} - 491 q^{16} - 491 q^{17} - 491 q^{18} - 491 q^{19} - 491 q^{20} - 491 q^{21} - 491 q^{22} - 491 q^{23} - 491 q^{24} - 491 q^{25} - 491 q^{26} - 491 q^{27} - 491 q^{28} - 491 q^{29} - 491 q^{30} - 491 q^{31} - 491 q^{32} - 491 q^{33} - 491 q^{34} - 491 q^{35} - 491 q^{36} - 491 q^{37} - 491 q^{38} - 491 q^{39} - 491 q^{40} - 491 q^{41} - 491 q^{42} - 491 q^{43} - 491 q^{44} - 491 q^{45} - 491 q^{46} - 491 q^{47} - 491 q^{48} - 491 q^{49} - 491 q^{50} - 491 q^{51} - 491 q^{52} - 491 q^{53} - 491 q^{54} - 491 q^{55} - 491 q^{56} - 491 q^{57} - 491 q^{58} - 491 q^{59} - 491 q^{60} - 491 q^{61} - 491 q^{62} - 491 q^{63} - 491 q^{64} - 491 q^{65} - 491 q^{66} - 491 q^{67} - 491 q^{68} - 491 q^{69} - 491 q^{70} - 491 q^{71} - 491 q^{72} - 491 q^{73} - 491 q^{74} - 491 q^{75} - 491 q^{76} - 491 q^{77} - 491 q^{78} - 491 q^{79} - 491 q^{80} - 491 q^{81} - 491 q^{82} - 491 q^{83} - 491 q^{84} - 491 q^{85} - 491 q^{86} - 491 q^{87} - 491 q^{88} - 491 q^{89} - 491 q^{90} - 491 q^{91} - 491 q^{92} - 491 q^{93} - 491 q^{94} - 491 q^{95} - 491 q^{96} - 491 q^{97} - 491 q^{98} - 491 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(983))\)

We only show spaces with even 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
983.4.a \(\chi_{983}(1, \cdot)\) 983.4.a.a 109 1
983.4.a.b 136
983.4.c \(\chi_{983}(2, \cdot)\) n/a 120050 490

"n/a" means that newforms for that character have not been added to the database yet