Defining parameters
| Level: | \( N \) | \(=\) | \( 38025 = 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 38025.hm (of order \(60\) and degree \(16\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 2925 \) |
| Character field: | \(\Q(\zeta_{60})\) | ||
| Sturm bound: | \(10920\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(38025, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 87808 | 74240 | 13568 |
| Cusp forms | 86912 | 73600 | 13312 |
| Eisenstein series | 896 | 640 | 256 |
Decomposition of \(S_{2}^{\mathrm{new}}(38025, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(38025, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(38025, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(2925, [\chi])\)\(^{\oplus 2}\)