Defining parameters
Level: | \( N \) | \(=\) | \( 592 = 2^{4} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 592.k (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 37 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(228\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(592, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 316 | 78 | 238 |
Cusp forms | 292 | 74 | 218 |
Eisenstein series | 24 | 4 | 20 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(592, [\chi])\) into newform subspaces
Decomposition of \(S_{3}^{\mathrm{old}}(592, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(592, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 2}\)