Defining parameters
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(512\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3072, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 80 | 12 | 68 |
Cusp forms | 32 | 4 | 28 |
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.e.a | $2$ | $1.533$ | \(\Q(\sqrt{2}) \) | $D_{4}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q-q^{3}-\beta q^{7}+q^{9}-\beta q^{13}+\beta q^{21}+\cdots\) |
3072.1.e.b | $2$ | $1.533$ | \(\Q(\sqrt{2}) \) | $D_{4}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+q^{3}-\beta q^{7}+q^{9}+\beta q^{13}-\beta q^{21}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3072, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3072, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1536, [\chi])\)\(^{\oplus 2}\)