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Properties

Label 31.3
Level 31
Weight 3
Dimension 65
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 240
Trace bound 1

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Defining parameters

Level: \( N \) = \( 31 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(240\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(31))\).

Total New Old
Modular forms 95 95 0
Cusp forms 65 65 0
Eisenstein series 30 30 0

Trace form

\( 65 q - 15 q^{2} - 15 q^{3} - 15 q^{4} - 15 q^{5} - 15 q^{6} - 15 q^{7} - 15 q^{8} - 15 q^{9} + O(q^{10}) \) \( 65 q - 15 q^{2} - 15 q^{3} - 15 q^{4} - 15 q^{5} - 15 q^{6} - 15 q^{7} - 15 q^{8} - 15 q^{9} - 15 q^{10} - 15 q^{11} - 15 q^{12} - 15 q^{13} - 15 q^{14} - 15 q^{15} - 15 q^{16} - 15 q^{17} - 15 q^{18} - 15 q^{19} - 15 q^{20} + 30 q^{21} + 225 q^{22} + 90 q^{23} + 345 q^{24} + 160 q^{25} + 105 q^{26} + 120 q^{27} + 145 q^{28} + 15 q^{29} - 45 q^{31} - 210 q^{32} - 105 q^{33} - 255 q^{34} - 165 q^{35} - 495 q^{36} - 330 q^{37} - 255 q^{38} - 330 q^{39} - 615 q^{40} - 180 q^{41} - 375 q^{42} - 80 q^{43} - 15 q^{44} - 15 q^{45} - 15 q^{46} - 15 q^{47} + 570 q^{48} + 345 q^{49} + 810 q^{50} + 885 q^{51} + 660 q^{52} + 225 q^{53} + 1140 q^{54} + 345 q^{55} + 660 q^{56} + 345 q^{57} + 300 q^{58} + 45 q^{59} + 270 q^{60} - 105 q^{62} - 270 q^{63} - 345 q^{64} - 375 q^{65} - 1140 q^{66} - 195 q^{67} - 750 q^{68} - 735 q^{69} - 1230 q^{70} - 615 q^{71} - 1830 q^{72} - 375 q^{73} - 990 q^{74} - 1020 q^{75} - 340 q^{76} + 180 q^{77} + 480 q^{78} + 440 q^{79} + 1785 q^{80} + 645 q^{81} + 585 q^{82} + 930 q^{83} + 1425 q^{84} + 405 q^{85} + 705 q^{86} + 285 q^{87} + 705 q^{88} + 210 q^{89} + 480 q^{90} + 50 q^{91} - 135 q^{93} - 150 q^{94} - 375 q^{95} - 870 q^{96} - 340 q^{97} - 1095 q^{98} - 540 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(31))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
31.3.b \(\chi_{31}(30, \cdot)\) 31.3.b.a 2 1
31.3.b.b 3
31.3.e \(\chi_{31}(6, \cdot)\) 31.3.e.a 2 2
31.3.e.b 6
31.3.f \(\chi_{31}(15, \cdot)\) 31.3.f.a 20 4
31.3.h \(\chi_{31}(3, \cdot)\) 31.3.h.a 32 8