Defining parameters
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.eg (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 336 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(10\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3024, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 80 | 16 | 64 |
Cusp forms | 32 | 16 | 16 |
Eisenstein series | 48 | 0 | 48 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 0 | 0 | 16 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3024, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3024.1.eg.a | $8$ | $1.509$ | \(\Q(\zeta_{24})\) | $S_{4}$ | None | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{7}q^{5}-\zeta_{24}^{6}q^{7}+\cdots\) |
3024.1.eg.b | $8$ | $1.509$ | \(\Q(\zeta_{24})\) | $S_{4}$ | None | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{10}q^{7}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3024, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)