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Properties

Label 317.2
Level 317
Weight 2
Dimension 4030
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 16748
Trace bound 2

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Defining parameters

Level: \( N \) = \( 317 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(16748\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(317))\).

Total New Old
Modular forms 4345 4345 0
Cusp forms 4030 4030 0
Eisenstein series 315 315 0

Trace form

\( 4030 q - 155 q^{2} - 154 q^{3} - 151 q^{4} - 152 q^{5} - 146 q^{6} - 150 q^{7} - 143 q^{8} - 145 q^{9} + O(q^{10}) \) \( 4030 q - 155 q^{2} - 154 q^{3} - 151 q^{4} - 152 q^{5} - 146 q^{6} - 150 q^{7} - 143 q^{8} - 145 q^{9} - 140 q^{10} - 146 q^{11} - 130 q^{12} - 144 q^{13} - 134 q^{14} - 134 q^{15} - 127 q^{16} - 140 q^{17} - 119 q^{18} - 138 q^{19} - 116 q^{20} - 126 q^{21} - 122 q^{22} - 134 q^{23} - 98 q^{24} - 127 q^{25} - 116 q^{26} - 118 q^{27} - 102 q^{28} - 128 q^{29} - 86 q^{30} - 126 q^{31} - 95 q^{32} - 110 q^{33} - 104 q^{34} - 110 q^{35} - 67 q^{36} - 120 q^{37} - 98 q^{38} - 102 q^{39} - 68 q^{40} - 116 q^{41} - 62 q^{42} - 114 q^{43} - 74 q^{44} - 80 q^{45} - 86 q^{46} - 110 q^{47} - 34 q^{48} - 101 q^{49} - 65 q^{50} - 86 q^{51} - 60 q^{52} - 104 q^{53} - 38 q^{54} - 86 q^{55} - 38 q^{56} - 78 q^{57} - 68 q^{58} - 98 q^{59} + 10 q^{60} - 96 q^{61} - 62 q^{62} - 54 q^{63} - 31 q^{64} - 74 q^{65} - 14 q^{66} - 90 q^{67} - 32 q^{68} - 62 q^{69} - 14 q^{70} - 86 q^{71} + 37 q^{72} - 84 q^{73} - 44 q^{74} - 34 q^{75} - 18 q^{76} - 62 q^{77} + 10 q^{78} - 78 q^{79} + 28 q^{80} - 37 q^{81} - 32 q^{82} - 74 q^{83} + 66 q^{84} - 50 q^{85} - 26 q^{86} - 38 q^{87} + 22 q^{88} - 68 q^{89} + 76 q^{90} - 46 q^{91} + 10 q^{92} - 30 q^{93} - 14 q^{94} - 38 q^{95} + 94 q^{96} - 60 q^{97} + 13 q^{98} - 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(317))\)

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
317.2.a \(\chi_{317}(1, \cdot)\) 317.2.a.a 11 1
317.2.a.b 15
317.2.b \(\chi_{317}(316, \cdot)\) 317.2.b.a 26 1
317.2.d \(\chi_{317}(10, \cdot)\) 317.2.d.a 1950 78
317.2.e \(\chi_{317}(4, \cdot)\) 317.2.e.a 2028 78