Properties

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

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Defining parameters

Level: \( N \) = \( 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newforms: \( 4 \)
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

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

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 the 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