Defining parameters
| Level: | \( N \) | \(=\) | \( 4096 = 2^{12} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 4096.k (of order \(32\) and degree \(16\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 128 \) |
| Character field: | \(\Q(\zeta_{32})\) | ||
| Sturm bound: | \(1024\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4096, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 8704 | 2176 | 6528 |
| Cusp forms | 7680 | 1920 | 5760 |
| Eisenstein series | 1024 | 256 | 768 |
Decomposition of \(S_{2}^{\mathrm{new}}(4096, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(4096, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4096, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(512, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1024, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2048, [\chi])\)\(^{\oplus 2}\)