Defining parameters
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.s (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(14\) | ||
Distinguishing \(T_p\): | \(2\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(525, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 344 | 96 | 248 |
Cusp forms | 296 | 96 | 200 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(525, [\chi])\) into newform subspaces
Decomposition of \(S_{3}^{\mathrm{old}}(525, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)