Defining parameters
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(64\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(64))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 62 | 15 | 47 |
Cusp forms | 50 | 13 | 37 |
Eisenstein series | 12 | 2 | 10 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | Dim |
---|---|
\(+\) | \(7\) |
\(-\) | \(6\) |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(64))\) into newform subspaces
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(64))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_0(64)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)