Defining parameters
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.i (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(210, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 688 | 72 | 616 |
Cusp forms | 656 | 72 | 584 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(210, [\chi])\) into newform subspaces
Decomposition of \(S_{8}^{\mathrm{old}}(210, [\chi])\) into lower level spaces
\( S_{8}^{\mathrm{old}}(210, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)