Defining parameters
Level: | \( N \) | \(=\) | \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3528.bg (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 72 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(672\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3528, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 28 | 12 |
Cusp forms | 8 | 8 | 0 |
Eisenstein series | 32 | 20 | 12 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 8 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3528, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3528.1.bg.a | $8$ | $1.761$ | \(\Q(\zeta_{24})\) | $D_{12}$ | \(\Q(\sqrt{-14}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}^{10}q^{2}+\zeta_{24}^{9}q^{3}-\zeta_{24}^{8}q^{4}+\cdots\) |