Defining parameters
Level: | \( N \) | = | \( 128 = 2^{7} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 5 \) | ||
Newform subspaces: | \( 11 \) | ||
Sturm bound: | \(2048\) | ||
Trace bound: | \(9\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(128))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 592 | 312 | 280 |
Cusp forms | 433 | 264 | 169 |
Eisenstein series | 159 | 48 | 111 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)
We only show spaces with even 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 \(S_{2}^{\mathrm{old}}(\Gamma_1(128))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(128)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)