Defining parameters
| Level: | \( N \) | \(=\) | \( 14700 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 14700.ez (of order \(60\) and degree \(16\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 525 \) |
| Character field: | \(\Q(\zeta_{60})\) | ||
| Sturm bound: | \(6720\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(14700, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 54528 | 6400 | 48128 |
| Cusp forms | 52992 | 6400 | 46592 |
| Eisenstein series | 1536 | 0 | 1536 |
Decomposition of \(S_{2}^{\mathrm{new}}(14700, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(14700, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(14700, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3675, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(7350, [\chi])\)\(^{\oplus 2}\)