Defining parameters
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 12 \) | ||
Sturm bound: | \(270\) | ||
Trace bound: | \(19\) | ||
Distinguishing \(T_p\): | \(2\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(675, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 198 | 48 | 150 |
Cusp forms | 162 | 48 | 114 |
Eisenstein series | 36 | 0 | 36 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(675, [\chi])\) into newform subspaces
Decomposition of \(S_{3}^{\mathrm{old}}(675, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(675, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)