Defining parameters
Level: | \( N \) | \(=\) | \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2700.bo (of order \(18\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 540 \) |
Character field: | \(\Q(\zeta_{18})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(540\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2700, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 96 | 24 | 72 |
Cusp forms | 24 | 0 | 24 |
Eisenstein series | 72 | 24 | 48 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 0 | 0 | 0 | 0 |
Decomposition of \(S_{1}^{\mathrm{old}}(2700, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2700, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)