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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

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

Display 100 coefficients 10 coefficients

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 available 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

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