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Properties

Label 31.2
Level 31
Weight 2
Dimension 26
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 160
Trace bound 2

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Defining parameters

Level: \( N \) = \( 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(160\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(31))\).

Total New Old
Modular forms 55 55 0
Cusp forms 26 26 0
Eisenstein series 29 29 0

Trace form

\( 26 q - 12 q^{2} - 11 q^{3} - 8 q^{4} - 9 q^{5} - 3 q^{6} - 7 q^{7} - 2 q^{9} + O(q^{10}) \) \( 26 q - 12 q^{2} - 11 q^{3} - 8 q^{4} - 9 q^{5} - 3 q^{6} - 7 q^{7} - 2 q^{9} + 3 q^{10} - 3 q^{11} + 13 q^{12} - q^{13} + 9 q^{14} + 9 q^{15} + 16 q^{16} + 3 q^{17} + 24 q^{18} + 5 q^{19} + 27 q^{20} + 12 q^{21} - 9 q^{22} - 6 q^{23} - 15 q^{24} - 19 q^{25} - 3 q^{26} - 20 q^{27} - 39 q^{28} - 15 q^{29} - 18 q^{30} - 14 q^{31} - 57 q^{32} + 3 q^{33} - 21 q^{34} + 3 q^{35} - 4 q^{36} - 22 q^{37} + 15 q^{38} + 6 q^{39} + 15 q^{40} + 12 q^{41} + 51 q^{42} + 24 q^{43} + 69 q^{44} + 63 q^{45} + 57 q^{46} + 33 q^{47} + 64 q^{48} + 12 q^{49} + 3 q^{50} - 33 q^{51} + 8 q^{52} + 9 q^{53} - 60 q^{54} - 3 q^{55} - 30 q^{56} - 25 q^{57} - 30 q^{58} + 15 q^{59} - 102 q^{60} - 58 q^{61} - 12 q^{62} - 46 q^{63} - 8 q^{64} - 21 q^{65} - 96 q^{66} + 23 q^{67} + 6 q^{68} - 9 q^{69} - 6 q^{70} - 3 q^{71} + 15 q^{72} + 29 q^{73} + 24 q^{74} + 4 q^{75} + 6 q^{77} + 18 q^{78} + 30 q^{79} + 21 q^{80} + 46 q^{81} + 51 q^{82} - 36 q^{83} + 29 q^{84} + 33 q^{85} - 3 q^{86} + 45 q^{87} - 15 q^{88} - 6 q^{90} + 32 q^{91} - 42 q^{92} - 11 q^{93} + 54 q^{94} - 15 q^{95} + 12 q^{96} + 18 q^{97} - 24 q^{98} + 66 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)

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
31.2.a \(\chi_{31}(1, \cdot)\) 31.2.a.a 2 1
31.2.c \(\chi_{31}(5, \cdot)\) 31.2.c.a 4 2
31.2.d \(\chi_{31}(2, \cdot)\) 31.2.d.a 4 4
31.2.g \(\chi_{31}(7, \cdot)\) 31.2.g.a 16 8