Defining parameters
Level: | \( N \) | \(=\) | \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2700.r (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 36 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Sturm bound: | \(1080\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2700, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1152 | 240 | 912 |
Cusp forms | 1008 | 216 | 792 |
Eisenstein series | 144 | 24 | 120 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(2700, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(2700, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)