Defining parameters
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 24 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(1152\) | ||
Trace bound: | \(49\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(23\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1728, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 900 | 96 | 804 |
Cusp forms | 828 | 96 | 732 |
Eisenstein series | 72 | 0 | 72 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1728, [\chi])\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)