Defining parameters
Level: | \( N \) | = | \( 55 = 5 \cdot 11 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 1 \) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(55))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 41 | 27 | 14 |
Cusp forms | 1 | 1 | 0 |
Eisenstein series | 40 | 26 | 14 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 1 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)
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 |
---|---|---|---|---|
55.1.c | \(\chi_{55}(21, \cdot)\) | None | 0 | 1 |
55.1.d | \(\chi_{55}(54, \cdot)\) | 55.1.d.a | 1 | 1 |
55.1.f | \(\chi_{55}(12, \cdot)\) | None | 0 | 2 |
55.1.h | \(\chi_{55}(19, \cdot)\) | None | 0 | 4 |
55.1.i | \(\chi_{55}(6, \cdot)\) | None | 0 | 4 |
55.1.k | \(\chi_{55}(3, \cdot)\) | None | 0 | 8 |