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Properties

Label 87.3
Level 87
Weight 3
Dimension 392
Nonzero newspaces 6
Newform subspaces 9
Sturm bound 1680
Trace bound 3

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Defining parameters

Level: \( N \) = \( 87 = 3 \cdot 29 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 9 \)
Sturm bound: \(1680\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(87))\).

Total New Old
Modular forms 616 444 172
Cusp forms 504 392 112
Eisenstein series 112 52 60

Trace form

\( 392 q - 14 q^{3} - 28 q^{4} - 14 q^{6} - 28 q^{7} - 14 q^{9} + O(q^{10}) \) \( 392 q - 14 q^{3} - 28 q^{4} - 14 q^{6} - 28 q^{7} - 14 q^{9} - 28 q^{10} - 14 q^{12} - 28 q^{13} - 14 q^{15} - 28 q^{16} - 14 q^{18} - 28 q^{19} - 336 q^{20} - 210 q^{21} - 364 q^{22} - 140 q^{23} - 350 q^{24} - 196 q^{25} - 140 q^{26} - 56 q^{27} - 56 q^{28} + 56 q^{29} + 140 q^{30} + 140 q^{31} + 448 q^{32} + 196 q^{33} + 392 q^{34} + 392 q^{35} + 658 q^{36} + 224 q^{37} + 560 q^{38} + 294 q^{39} + 476 q^{40} - 14 q^{42} - 28 q^{43} - 364 q^{44} - 182 q^{45} - 1568 q^{46} - 560 q^{47} - 1022 q^{48} - 924 q^{49} - 1372 q^{50} - 350 q^{51} - 1148 q^{52} - 504 q^{53} - 14 q^{54} - 476 q^{55} - 196 q^{56} - 28 q^{57} + 308 q^{58} + 112 q^{59} + 546 q^{60} + 420 q^{61} + 980 q^{62} + 154 q^{63} + 1736 q^{64} + 1008 q^{65} + 994 q^{66} + 1092 q^{67} + 2156 q^{68} + 658 q^{69} + 2884 q^{70} + 784 q^{71} + 1582 q^{72} + 1092 q^{73} + 476 q^{74} + 756 q^{75} - 28 q^{76} + 882 q^{78} - 28 q^{79} + 546 q^{81} - 28 q^{82} + 196 q^{84} - 28 q^{85} - 84 q^{87} - 56 q^{88} - 574 q^{90} - 28 q^{91} - 406 q^{93} - 28 q^{94} - 2772 q^{96} - 1792 q^{97} - 2380 q^{98} - 2716 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(87))\)

We only show spaces with odd 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
87.3.b \(\chi_{87}(59, \cdot)\) 87.3.b.a 18 1
87.3.d \(\chi_{87}(86, \cdot)\) 87.3.d.a 3 1
87.3.d.b 3
87.3.d.c 12
87.3.e \(\chi_{87}(46, \cdot)\) 87.3.e.a 8 2
87.3.e.b 12
87.3.h \(\chi_{87}(5, \cdot)\) 87.3.h.a 108 6
87.3.j \(\chi_{87}(20, \cdot)\) 87.3.j.a 108 6
87.3.l \(\chi_{87}(10, \cdot)\) 87.3.l.a 120 12

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(87))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(87)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)