Defining parameters
Level: | \( N \) | = | \( 88 = 2^{3} \cdot 11 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 1 \) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(88))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 66 | 22 | 44 |
Cusp forms | 6 | 4 | 2 |
Eisenstein series | 60 | 18 | 42 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(88))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
88.1.b | \(\chi_{88}(21, \cdot)\) | None | 0 | 1 |
88.1.d | \(\chi_{88}(23, \cdot)\) | None | 0 | 1 |
88.1.f | \(\chi_{88}(67, \cdot)\) | None | 0 | 1 |
88.1.h | \(\chi_{88}(65, \cdot)\) | None | 0 | 1 |
88.1.j | \(\chi_{88}(17, \cdot)\) | None | 0 | 4 |
88.1.l | \(\chi_{88}(3, \cdot)\) | 88.1.l.a | 4 | 4 |
88.1.n | \(\chi_{88}(15, \cdot)\) | None | 0 | 4 |
88.1.p | \(\chi_{88}(13, \cdot)\) | None | 0 | 4 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(88))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(88)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 2}\)