Defining parameters
Level: | \( N \) | = | \( 656 = 2^{4} \cdot 41 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(26880\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(656))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 655 | 192 | 463 |
Cusp forms | 95 | 16 | 79 |
Eisenstein series | 560 | 176 | 384 |
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 \(S_{1}^{\mathrm{new}}(\Gamma_1(656))\)
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.
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(656))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(656)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(328))\)\(^{\oplus 2}\)