Defining parameters
| Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1470.bq (of order \(42\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 245 \) |
| Character field: | \(\Q(\zeta_{42})\) | ||
| Sturm bound: | \(672\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1470, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 4128 | 672 | 3456 |
| Cusp forms | 3936 | 672 | 3264 |
| Eisenstein series | 192 | 0 | 192 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1470, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(1470, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1470, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)