Defining parameters
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(49\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(17\), \(41\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1728, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 324 | 32 | 292 |
Cusp forms | 252 | 32 | 220 |
Eisenstein series | 72 | 0 | 72 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1728, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1728, [\chi]) \cong \)