Defining parameters
| Level: | \( N \) | \(=\) | \( 6900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 23 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 6900.bo (of order \(11\) and degree \(10\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 23 \) |
| Character field: | \(\Q(\zeta_{11})\) | ||
| Sturm bound: | \(2880\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(6900, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 14760 | 760 | 14000 |
| Cusp forms | 14040 | 760 | 13280 |
| Eisenstein series | 720 | 0 | 720 |
Decomposition of \(S_{2}^{\mathrm{new}}(6900, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(6900, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(6900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1380, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1725, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3450, [\chi])\)\(^{\oplus 2}\)