Defining parameters
Level: | \( N \) | \(=\) | \( 4096 = 2^{12} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4096.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 19 \) | ||
Sturm bound: | \(1024\) | ||
Trace bound: | \(65\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(7\), \(23\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4096))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 560 | 136 | 424 |
Cusp forms | 465 | 120 | 345 |
Eisenstein series | 95 | 16 | 79 |
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 |
---|---|
\(+\) | \(56\) |
\(-\) | \(64\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4096))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4096))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4096)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(256))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(512))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1024))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2048))\)\(^{\oplus 2}\)