Defining parameters
Level: | \( N \) | \(=\) | \( 3584 = 2^{9} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3584.bm (of order \(32\) and degree \(16\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 896 \) |
Character field: | \(\Q(\zeta_{32})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(512\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3584, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 192 | 48 | 144 |
Cusp forms | 64 | 16 | 48 |
Eisenstein series | 128 | 32 | 96 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 16 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3584, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3584.1.bm.a | $16$ | $1.789$ | \(\Q(\zeta_{32})\) | $D_{32}$ | \(\Q(\sqrt{-7}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{32}^{5}q^{7}+\zeta_{32}^{3}q^{9}+(\zeta_{32}^{6}+\zeta_{32}^{15}+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3584, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3584, [\chi]) \cong \)