Properties

Label 87.2
Level 87
Weight 2
Dimension 181
Nonzero newspaces 6
Newform subspaces 10
Sturm bound 1120
Trace bound 1

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Defining parameters

Level: \( N \) = \( 87 = 3 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 10 \)
Sturm bound: \(1120\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(87))\).

Total New Old
Modular forms 336 237 99
Cusp forms 225 181 44
Eisenstein series 111 56 55

Trace form

\( 181q - 3q^{2} - 15q^{3} - 35q^{4} - 6q^{5} - 17q^{6} - 36q^{7} - 15q^{8} - 15q^{9} + O(q^{10}) \) \( 181q - 3q^{2} - 15q^{3} - 35q^{4} - 6q^{5} - 17q^{6} - 36q^{7} - 15q^{8} - 15q^{9} - 46q^{10} - 12q^{11} - 21q^{12} - 42q^{13} - 24q^{14} - 20q^{15} - 59q^{16} - 18q^{17} - 17q^{18} - 48q^{19} + 6q^{21} - 8q^{22} + 4q^{23} + 55q^{24} - 3q^{25} + 28q^{26} + 27q^{27} + 56q^{28} + 27q^{29} + 38q^{30} - 4q^{31} + 49q^{32} + 16q^{33} - 12q^{34} + 8q^{35} + 63q^{36} - 38q^{37} - 4q^{38} - 76q^{40} - 42q^{41} - 38q^{42} - 72q^{43} - 56q^{44} - 6q^{45} + 40q^{46} + 8q^{47} + 67q^{48} + 27q^{49} + 103q^{50} + 24q^{51} + 98q^{52} + 72q^{53} - 17q^{54} + 124q^{55} + 76q^{56} + 36q^{57} + 221q^{58} - 4q^{59} + 140q^{60} + 22q^{61} + 100q^{62} + 6q^{63} + 97q^{64} + 42q^{65} + 62q^{66} + 16q^{67} + 70q^{68} + 18q^{69} + 52q^{70} - 16q^{71} - 85q^{72} - 32q^{73} - 86q^{74} - 115q^{75} - 168q^{76} - 96q^{77} - 168q^{78} - 108q^{79} - 186q^{80} - 127q^{81} - 154q^{82} - 84q^{83} - 196q^{84} - 136q^{85} - 132q^{86} - 113q^{87} - 236q^{88} - 90q^{89} - 172q^{90} - 140q^{91} - 168q^{92} - 102q^{93} - 172q^{94} - 120q^{95} - 231q^{96} - 28q^{97} - 31q^{98} + 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)

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
87.2.a \(\chi_{87}(1, \cdot)\) 87.2.a.a 2 1
87.2.a.b 3
87.2.c \(\chi_{87}(28, \cdot)\) 87.2.c.a 4 1
87.2.f \(\chi_{87}(17, \cdot)\) 87.2.f.a 4 2
87.2.f.b 4
87.2.f.c 8
87.2.g \(\chi_{87}(7, \cdot)\) 87.2.g.a 18 6
87.2.g.b 18
87.2.i \(\chi_{87}(4, \cdot)\) 87.2.i.a 24 6
87.2.k \(\chi_{87}(2, \cdot)\) 87.2.k.a 96 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(87))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(87)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)