Defining parameters
| Level: | \( N \) | \(=\) | \( 7500 = 2^{2} \cdot 3 \cdot 5^{4} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 7500.bh (of order \(100\) and degree \(40\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 500 \) |
| Character field: | \(\Q(\zeta_{100})\) | ||
| Sturm bound: | \(3000\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(7500, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 60800 | 18000 | 42800 |
| Cusp forms | 59200 | 18000 | 41200 |
| Eisenstein series | 1600 | 0 | 1600 |
Decomposition of \(S_{2}^{\mathrm{new}}(7500, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(7500, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(7500, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1500, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2500, [\chi])\)\(^{\oplus 2}\)