Defining parameters
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.kv (of order \(42\) and degree \(12\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 381 \) |
Character field: | \(\Q(\zeta_{42})\) | ||
Sturm bound: | \(2048\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8001, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 12384 | 3072 | 9312 |
Cusp forms | 12192 | 3072 | 9120 |
Eisenstein series | 192 | 0 | 192 |
Decomposition of \(S_{2}^{\mathrm{new}}(8001, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8001, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8001, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(381, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1143, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2667, [\chi])\)\(^{\oplus 2}\)