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Properties

Label 31.10
Level 31
Weight 10
Dimension 345
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 800
Trace bound 1

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Defining parameters

Level: \( N \) = \( 31 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(800\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(31))\).

Total New Old
Modular forms 375 373 2
Cusp forms 345 345 0
Eisenstein series 30 28 2

Trace form

\( 345 q - 15 q^{2} - 15 q^{3} - 15 q^{4} - 15 q^{5} - 15 q^{6} - 15 q^{7} - 15 q^{8} - 15 q^{9} + O(q^{10}) \) \( 345 q - 15 q^{2} - 15 q^{3} - 15 q^{4} - 15 q^{5} - 15 q^{6} - 15 q^{7} - 15 q^{8} - 15 q^{9} - 15 q^{10} - 15 q^{11} - 15 q^{12} - 15 q^{13} - 15 q^{14} - 15 q^{15} - 15 q^{16} - 15 q^{17} - 15 q^{18} - 15 q^{19} - 15 q^{20} - 5094915 q^{21} + 13093905 q^{22} - 2898885 q^{23} - 23639055 q^{24} - 15 q^{25} + 13178385 q^{26} + 21848115 q^{27} + 7004145 q^{28} - 14274135 q^{29} - 48600030 q^{30} - 19194315 q^{31} + 2741730 q^{32} + 26613345 q^{33} + 85354545 q^{34} + 35137485 q^{35} - 15 q^{36} - 74359635 q^{37} - 81999855 q^{38} - 67115805 q^{39} + 86399985 q^{40} + 82124385 q^{41} + 83941905 q^{42} - 120262605 q^{43} - 15 q^{44} - 15 q^{45} - 15 q^{46} - 15 q^{47} + 27045300 q^{48} + 331606035 q^{49} + 123747660 q^{50} - 653778105 q^{51} - 685161990 q^{52} - 141478605 q^{53} + 386279010 q^{54} + 493279125 q^{55} + 1404523650 q^{56} + 735073815 q^{57} + 256802370 q^{58} - 141343965 q^{59} - 2442063420 q^{60} - 1246125720 q^{61} - 1120525485 q^{62} - 801080790 q^{63} + 194314455 q^{64} + 1049716695 q^{65} + 4250225010 q^{66} + 631783395 q^{67} + 1721272020 q^{68} + 441102135 q^{69} - 1492307700 q^{70} - 1599040875 q^{71} - 5811312060 q^{72} - 896693805 q^{73} - 495166140 q^{74} + 353555205 q^{75} + 7027375410 q^{76} + 4578945975 q^{77} - 1760867790 q^{78} - 908513565 q^{79} - 7824998415 q^{80} - 3046855215 q^{81} - 1706650575 q^{82} + 360014955 q^{83} + 6009523185 q^{84} + 3164916225 q^{85} + 6829007985 q^{86} + 2730096825 q^{87} + 3921592305 q^{88} - 635358015 q^{89} - 6904003740 q^{90} - 3975583965 q^{91} - 12895073310 q^{92} - 8026885935 q^{93} - 2815819230 q^{94} - 1772883135 q^{95} + 4305419940 q^{96} + 4007142345 q^{97} + 16239049905 q^{98} + 7662738735 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(31))\)

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
31.10.a \(\chi_{31}(1, \cdot)\) 31.10.a.a 10 1
31.10.a.b 13
31.10.c \(\chi_{31}(5, \cdot)\) 31.10.c.a 46 2
31.10.d \(\chi_{31}(2, \cdot)\) 31.10.d.a 92 4
31.10.g \(\chi_{31}(7, \cdot)\) 31.10.g.a 184 8