Defining parameters
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(630, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 448 | 44 | 404 |
Cusp forms | 416 | 44 | 372 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(630, [\chi])\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(630, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)