Defining parameters
Level: | \( N \) | = | \( 87 = 3 \cdot 29 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 1 \) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(560\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(87))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 58 | 28 | 30 |
Cusp forms | 2 | 2 | 0 |
Eisenstein series | 56 | 26 | 30 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 2 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(87))\)
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 |
---|---|---|---|---|
87.1.b | \(\chi_{87}(59, \cdot)\) | None | 0 | 1 |
87.1.d | \(\chi_{87}(86, \cdot)\) | 87.1.d.a | 1 | 1 |
87.1.d.b | 1 | |||
87.1.e | \(\chi_{87}(46, \cdot)\) | None | 0 | 2 |
87.1.h | \(\chi_{87}(5, \cdot)\) | None | 0 | 6 |
87.1.j | \(\chi_{87}(20, \cdot)\) | None | 0 | 6 |
87.1.l | \(\chi_{87}(10, \cdot)\) | None | 0 | 12 |