Defining parameters
Level: | \( N \) | = | \( 128 = 2^{7} \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 5 \) | ||
Newform subspaces: | \( 9 \) | ||
Sturm bound: | \(3072\) | ||
Trace bound: | \(9\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(128))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1104 | 600 | 504 |
Cusp forms | 944 | 552 | 392 |
Eisenstein series | 160 | 48 | 112 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(128))\)
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 \(S_{3}^{\mathrm{old}}(\Gamma_1(128))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(128)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)