Defining parameters
Level: | \( N \) | = | \( 52 = 2^{2} \cdot 13 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 1 \) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(168\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(52))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 32 | 12 | 20 |
Cusp forms | 2 | 2 | 0 |
Eisenstein series | 30 | 10 | 20 |
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 \(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)
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 |
---|---|---|---|---|
52.1.b | \(\chi_{52}(51, \cdot)\) | None | 0 | 1 |
52.1.c | \(\chi_{52}(27, \cdot)\) | None | 0 | 1 |
52.1.g | \(\chi_{52}(5, \cdot)\) | None | 0 | 2 |
52.1.i | \(\chi_{52}(23, \cdot)\) | None | 0 | 2 |
52.1.j | \(\chi_{52}(3, \cdot)\) | 52.1.j.a | 2 | 2 |
52.1.k | \(\chi_{52}(33, \cdot)\) | None | 0 | 4 |