Defining parameters
Level: | \( N \) | = | \( 64 = 2^{6} \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 15 \) | ||
Sturm bound: | \(2048\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(64))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 932 | 515 | 417 |
Cusp forms | 860 | 493 | 367 |
Eisenstein series | 72 | 22 | 50 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(64))\)
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 available newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
64.8.a | \(\chi_{64}(1, \cdot)\) | 64.8.a.a | 1 | 1 |
64.8.a.b | 1 | |||
64.8.a.c | 1 | |||
64.8.a.d | 1 | |||
64.8.a.e | 1 | |||
64.8.a.f | 1 | |||
64.8.a.g | 1 | |||
64.8.a.h | 2 | |||
64.8.a.i | 2 | |||
64.8.a.j | 2 | |||
64.8.b | \(\chi_{64}(33, \cdot)\) | 64.8.b.a | 2 | 1 |
64.8.b.b | 4 | |||
64.8.b.c | 8 | |||
64.8.e | \(\chi_{64}(17, \cdot)\) | 64.8.e.a | 26 | 2 |
64.8.g | \(\chi_{64}(9, \cdot)\) | None | 0 | 4 |
64.8.i | \(\chi_{64}(5, \cdot)\) | 64.8.i.a | 440 | 8 |
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(64)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)