Defining parameters
Level: | \( N \) | \(=\) | \( 7168 = 2^{10} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7168.ba (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 112 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Sturm bound: | \(2048\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(7168, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 4288 | 1056 | 3232 |
Cusp forms | 3904 | 992 | 2912 |
Eisenstein series | 384 | 64 | 320 |
Decomposition of \(S_{2}^{\mathrm{new}}(7168, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(7168, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(7168, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1792, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3584, [\chi])\)\(^{\oplus 2}\)