Defining parameters
| Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 9 \) |
| Character orbit: | \([\chi]\) | \(=\) | 300.s (of order \(10\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 75 \) |
| Character field: | \(\Q(\zeta_{10})\) | ||
| Sturm bound: | \(540\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(300, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1944 | 320 | 1624 |
| Cusp forms | 1896 | 320 | 1576 |
| Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(300, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{9}^{\mathrm{old}}(300, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(300, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)