Defining parameters
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 24 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(512\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3072, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 86 | 12 | 74 |
Cusp forms | 38 | 4 | 34 |
Eisenstein series | 48 | 8 | 40 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3072, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3072.1.h.a | $4$ | $1.533$ | \(\Q(\zeta_{8})\) | $D_{4}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{8}^{2}q^{3}+(\zeta_{8}-\zeta_{8}^{3})q^{7}-q^{9}+(\zeta_{8}+\cdots)q^{13}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3072, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3072, [\chi]) \cong \)