Defining parameters
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.cq (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 84 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(768\) | ||
Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1008, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1200 | 96 | 1104 |
Cusp forms | 1104 | 96 | 1008 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1008.4.cq.a | $32$ | $59.474$ | None | \(0\) | \(0\) | \(0\) | \(-36\) | ||
1008.4.cq.b | $32$ | $59.474$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
1008.4.cq.c | $32$ | $59.474$ | None | \(0\) | \(0\) | \(0\) | \(36\) |
Decomposition of \(S_{4}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)