Defining parameters
Level: | \( N \) | = | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 5 \) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(37632\) | ||
Trace bound: | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(784))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 895 | 234 | 661 |
Cusp forms | 55 | 16 | 39 |
Eisenstein series | 840 | 218 | 622 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 16 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(784))\)
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.
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(784))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(784)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 2}\)