Defining parameters
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 16 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(21\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(11\), \(19\), \(37\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(768, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 280 | 68 | 212 |
Cusp forms | 232 | 60 | 172 |
Eisenstein series | 48 | 8 | 40 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(768, [\chi])\) into newform subspaces
Decomposition of \(S_{3}^{\mathrm{old}}(768, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(768, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)