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Properties

Label 87.4
Level 87
Weight 4
Dimension 602
Nonzero newspaces 6
Newform subspaces 10
Sturm bound 2240
Trace bound 1

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Defining parameters

Level: \( N \) = \( 87 = 3 \cdot 29 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 10 \)
Sturm bound: \(2240\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(87))\).

Total New Old
Modular forms 896 658 238
Cusp forms 784 602 182
Eisenstein series 112 56 56

Trace form

\( 602 q - 14 q^{3} - 28 q^{4} - 14 q^{6} - 28 q^{7} - 14 q^{9} + O(q^{10}) \) \( 602 q - 14 q^{3} - 28 q^{4} - 14 q^{6} - 28 q^{7} - 14 q^{9} - 28 q^{10} - 14 q^{12} - 28 q^{13} - 14 q^{15} - 28 q^{16} - 14 q^{18} - 28 q^{19} + 1848 q^{20} + 770 q^{21} + 756 q^{22} + 56 q^{23} - 686 q^{24} - 924 q^{25} - 1540 q^{26} - 1106 q^{27} - 3136 q^{28} - 1568 q^{29} - 2212 q^{30} - 1260 q^{31} - 1792 q^{32} - 350 q^{33} + 112 q^{34} + 784 q^{35} + 2338 q^{36} + 1204 q^{37} + 3472 q^{38} + 2282 q^{39} + 4340 q^{40} - 14 q^{42} - 28 q^{43} + 3500 q^{44} + 1372 q^{45} + 10472 q^{46} + 2968 q^{47} + 3682 q^{48} + 1652 q^{49} - 196 q^{50} - 854 q^{51} - 6076 q^{52} - 4662 q^{53} - 14 q^{54} - 11452 q^{55} - 10780 q^{56} - 3192 q^{57} - 19180 q^{58} - 3080 q^{59} - 8470 q^{60} - 5068 q^{61} - 7252 q^{62} - 770 q^{63} - 3808 q^{64} - 126 q^{65} + 1666 q^{66} + 3668 q^{67} + 10388 q^{68} + 4186 q^{69} + 22148 q^{70} + 7000 q^{71} - 6146 q^{72} + 12782 q^{73} + 6020 q^{74} - 3234 q^{75} - 28 q^{76} + 1554 q^{78} - 28 q^{79} + 6258 q^{81} - 28 q^{82} + 13804 q^{84} - 28 q^{85} + 6006 q^{87} - 56 q^{88} + 10346 q^{90} - 28 q^{91} + 2450 q^{93} - 28 q^{94} + 10332 q^{96} + 22218 q^{97} + 26740 q^{98} + 12670 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(87))\)

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
87.4.a \(\chi_{87}(1, \cdot)\) 87.4.a.a 2 1
87.4.a.b 2
87.4.a.c 5
87.4.a.d 5
87.4.c \(\chi_{87}(28, \cdot)\) 87.4.c.a 16 1
87.4.f \(\chi_{87}(17, \cdot)\) 87.4.f.a 56 2
87.4.g \(\chi_{87}(7, \cdot)\) 87.4.g.a 42 6
87.4.g.b 42
87.4.i \(\chi_{87}(4, \cdot)\) 87.4.i.a 96 6
87.4.k \(\chi_{87}(2, \cdot)\) 87.4.k.a 336 12

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(87))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(87)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 1}\)