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

\( 181 q - 3 q^{2} - 15 q^{3} - 35 q^{4} - 6 q^{5} - 17 q^{6} - 36 q^{7} - 15 q^{8} - 15 q^{9} - 46 q^{10} - 12 q^{11} - 21 q^{12} - 42 q^{13} - 24 q^{14} - 20 q^{15} - 59 q^{16} - 18 q^{17} - 17 q^{18} - 48 q^{19}+ \cdots + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

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