Defining parameters
| Level: | \( N \) | \(=\) | \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 7448.fr (of order \(21\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 49 \) |
| Character field: | \(\Q(\zeta_{21})\) | ||
| Sturm bound: | \(2240\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(7448, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 13536 | 3024 | 10512 |
| Cusp forms | 13344 | 3024 | 10320 |
| Eisenstein series | 192 | 0 | 192 |
Decomposition of \(S_{2}^{\mathrm{new}}(7448, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(7448, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(7448, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(931, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1862, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3724, [\chi])\)\(^{\oplus 2}\)