Properties

Label 86.2
Level 86
Weight 2
Dimension 76
Nonzero newspaces 4
Newform subspaces 8
Sturm bound 924
Trace bound 1

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Defining parameters

Level: \( N \) = \( 86 = 2 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 8 \)
Sturm bound: \(924\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(86))\).

Total New Old
Modular forms 273 76 197
Cusp forms 190 76 114
Eisenstein series 83 0 83

Trace form

\( 76q - q^{2} - 4q^{3} - q^{4} - 6q^{5} - 4q^{6} - 8q^{7} - q^{8} - 13q^{9} + O(q^{10}) \) \( 76q - q^{2} - 4q^{3} - q^{4} - 6q^{5} - 4q^{6} - 8q^{7} - q^{8} - 13q^{9} - 6q^{10} - 12q^{11} - 4q^{12} - 14q^{13} - 8q^{14} - 24q^{15} - q^{16} - 18q^{17} - 13q^{18} - 20q^{19} - 6q^{20} - 32q^{21} - 12q^{22} - 24q^{23} - 4q^{24} - 31q^{25} - 14q^{26} - 40q^{27} - 8q^{28} - 30q^{29} - 24q^{30} - 18q^{31} - q^{32} + 36q^{33} + 45q^{34} + 36q^{35} + 43q^{36} + 46q^{37} + 64q^{38} + 42q^{39} - 6q^{40} + 52q^{42} + 167q^{43} + 30q^{44} + 132q^{45} + 60q^{46} - 6q^{47} - 4q^{48} + 41q^{49} + 53q^{50} + 12q^{51} + 42q^{52} + 30q^{53} + 23q^{54} + 12q^{55} - 8q^{56} - 66q^{57} - 30q^{58} - 60q^{59} - 24q^{60} - 62q^{61} - 32q^{62} - 104q^{63} - q^{64} - 84q^{65} - 48q^{66} - 68q^{67} - 18q^{68} - 54q^{69} - 48q^{70} - 30q^{71} - 13q^{72} - 32q^{73} - 38q^{74} + 23q^{75} - 20q^{76} + 30q^{77} - 56q^{78} + 4q^{79} - 6q^{80} + 47q^{81} - 42q^{82} - 32q^{84} - 24q^{85} - 43q^{86} + 90q^{87} - 12q^{88} - 6q^{89} - 78q^{90} - 28q^{91} - 24q^{92} + 40q^{93} - 48q^{94} - 36q^{95} - 4q^{96} + 28q^{97} - 57q^{98} - 9q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(86))\)

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
86.2.a \(\chi_{86}(1, \cdot)\) 86.2.a.a 2 1
86.2.a.b 2
86.2.c \(\chi_{86}(49, \cdot)\) 86.2.c.a 2 2
86.2.c.b 4
86.2.e \(\chi_{86}(11, \cdot)\) 86.2.e.a 12 6
86.2.e.b 18
86.2.g \(\chi_{86}(9, \cdot)\) 86.2.g.a 12 12
86.2.g.b 24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(86))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(86)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 2}\)