Defining parameters
| Level: | \( N \) | \(=\) | \( 44100 = 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 44100.dy (of order \(10\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 525 \) |
| Character field: | \(\Q(\zeta_{10})\) | ||
| Sturm bound: | \(20160\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(44100, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 40704 | 1600 | 39104 |
| Cusp forms | 39936 | 1600 | 38336 |
| Eisenstein series | 768 | 0 | 768 |
Decomposition of \(S_{2}^{\mathrm{new}}(44100, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(44100, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(44100, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3675, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(6300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(7350, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(11025, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(14700, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(22050, [\chi])\)\(^{\oplus 2}\)