Defining parameters
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(864\) | ||
Trace bound: | \(49\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(11\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(1728, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 612 | 64 | 548 |
Cusp forms | 540 | 64 | 476 |
Eisenstein series | 72 | 0 | 72 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(1728, [\chi])\) into newform subspaces
Decomposition of \(S_{3}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)