Defining parameters
| Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1176.bx (of order \(42\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 147 \) |
| Character field: | \(\Q(\zeta_{42})\) | ||
| Sturm bound: | \(672\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(1176, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5472 | 1344 | 4128 |
| Cusp forms | 5280 | 1344 | 3936 |
| Eisenstein series | 192 | 0 | 192 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(1176, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{3}^{\mathrm{old}}(1176, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(1176, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)