Defining parameters
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.bo (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 105 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(630, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 896 | 96 | 800 |
Cusp forms | 832 | 96 | 736 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(630, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
630.4.bo.a | $48$ | $37.171$ | None | \(-48\) | \(0\) | \(-18\) | \(0\) | ||
630.4.bo.b | $48$ | $37.171$ | None | \(48\) | \(0\) | \(18\) | \(0\) |
Decomposition of \(S_{4}^{\mathrm{old}}(630, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)