Defining parameters
| Level: | \( N \) | \(=\) | \( 3136 = 2^{6} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3136.ca (of order \(42\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 392 \) |
| Character field: | \(\Q(\zeta_{42})\) | ||
| Sturm bound: | \(896\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3136, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5520 | 1344 | 4176 |
| Cusp forms | 5232 | 1344 | 3888 |
| Eisenstein series | 288 | 0 | 288 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3136, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(3136, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3136, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1568, [\chi])\)\(^{\oplus 2}\)