Defining parameters
| Level: | \( N \) | = | \( 64 = 2^{6} \) |
| Weight: | \( k \) | = | \( 24 \) |
| Nonzero newspaces: | \( 4 \) | ||
| Sturm bound: | \(6144\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_1(64))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2980 | 1667 | 1313 |
| Cusp forms | 2908 | 1645 | 1263 |
| Eisenstein series | 72 | 22 | 50 |
Trace form
Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_1(64))\)
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 |
|---|---|---|---|---|
| 64.24.a | \(\chi_{64}(1, \cdot)\) | 64.24.a.a | 1 | 1 |
| 64.24.a.b | 1 | |||
| 64.24.a.c | 1 | |||
| 64.24.a.d | 2 | |||
| 64.24.a.e | 2 | |||
| 64.24.a.f | 2 | |||
| 64.24.a.g | 2 | |||
| 64.24.a.h | 3 | |||
| 64.24.a.i | 3 | |||
| 64.24.a.j | 3 | |||
| 64.24.a.k | 3 | |||
| 64.24.a.l | 4 | |||
| 64.24.a.m | 6 | |||
| 64.24.a.n | 6 | |||
| 64.24.a.o | 6 | |||
| 64.24.b | \(\chi_{64}(33, \cdot)\) | 64.24.b.a | 2 | 1 |
| 64.24.b.b | 12 | |||
| 64.24.b.c | 32 | |||
| 64.24.e | \(\chi_{64}(17, \cdot)\) | 64.24.e.a | 90 | 2 |
| 64.24.g | \(\chi_{64}(9, \cdot)\) | None | 0 | 4 |
| 64.24.i | \(\chi_{64}(5, \cdot)\) | n/a | 1464 | 8 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_1(64))\) into lower level spaces
\( S_{24}^{\mathrm{old}}(\Gamma_1(64)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)