Defining parameters
| Level: | \( N \) | \(=\) | \( 24200 = 2^{3} \cdot 5^{2} \cdot 11^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 24200.mt (of order \(220\) and degree \(80\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 605 \) |
| Character field: | \(\Q(\zeta_{220})\) | ||
| Sturm bound: | \(7920\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(24200, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 318720 | 47520 | 271200 |
| Cusp forms | 314880 | 47520 | 267360 |
| Eisenstein series | 3840 | 0 | 3840 |
Decomposition of \(S_{2}^{\mathrm{new}}(24200, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(24200, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(24200, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1210, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2420, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3025, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4840, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(6050, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(12100, [\chi])\)\(^{\oplus 2}\)