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Properties

Label 239.4
Level 239
Weight 4
Dimension 7021
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 19040
Trace bound 1

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Defining parameters

Level: \( N \) = \( 239 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(19040\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(239))\).

Total New Old
Modular forms 7259 7257 2
Cusp forms 7021 7021 0
Eisenstein series 238 236 2

Trace form

\( 7021 q - 119 q^{2} - 119 q^{3} - 119 q^{4} - 119 q^{5} - 119 q^{6} - 119 q^{7} - 119 q^{8} - 119 q^{9} + O(q^{10}) \) \( 7021 q - 119 q^{2} - 119 q^{3} - 119 q^{4} - 119 q^{5} - 119 q^{6} - 119 q^{7} - 119 q^{8} - 119 q^{9} - 119 q^{10} - 119 q^{11} - 119 q^{12} - 119 q^{13} - 119 q^{14} - 119 q^{15} - 119 q^{16} - 119 q^{17} - 119 q^{18} - 119 q^{19} - 119 q^{20} - 119 q^{21} - 119 q^{22} - 119 q^{23} - 119 q^{24} - 119 q^{25} - 119 q^{26} - 119 q^{27} - 119 q^{28} - 119 q^{29} - 119 q^{30} - 119 q^{31} - 119 q^{32} - 119 q^{33} - 119 q^{34} - 119 q^{35} - 119 q^{36} - 119 q^{37} - 119 q^{38} - 119 q^{39} - 119 q^{40} - 119 q^{41} - 119 q^{42} - 119 q^{43} - 119 q^{44} - 119 q^{45} - 119 q^{46} - 119 q^{47} - 119 q^{48} - 119 q^{49} - 119 q^{50} - 119 q^{51} - 119 q^{52} - 119 q^{53} - 119 q^{54} - 119 q^{55} - 119 q^{56} - 119 q^{57} - 119 q^{58} - 119 q^{59} - 119 q^{60} - 119 q^{61} - 119 q^{62} - 119 q^{63} - 119 q^{64} - 119 q^{65} - 119 q^{66} - 119 q^{67} - 119 q^{68} - 119 q^{69} - 119 q^{70} - 119 q^{71} - 119 q^{72} - 119 q^{73} - 119 q^{74} - 119 q^{75} - 119 q^{76} - 119 q^{77} - 119 q^{78} - 119 q^{79} - 119 q^{80} - 119 q^{81} - 119 q^{82} - 119 q^{83} - 119 q^{84} - 119 q^{85} - 119 q^{86} - 119 q^{87} - 119 q^{88} - 119 q^{89} - 119 q^{90} - 119 q^{91} - 119 q^{92} - 119 q^{93} - 119 q^{94} - 119 q^{95} - 119 q^{96} - 119 q^{97} - 119 q^{98} - 119 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(239))\)

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
239.4.a \(\chi_{239}(1, \cdot)\) 239.4.a.a 22 1
239.4.a.b 37
239.4.c \(\chi_{239}(10, \cdot)\) 239.4.c.a 354 6
239.4.e \(\chi_{239}(6, \cdot)\) 239.4.e.a 944 16
239.4.g \(\chi_{239}(2, \cdot)\) 239.4.g.a 5664 96