Defining parameters
Level: | \( N \) | \(=\) | \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3528.ce (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 504 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(672\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3528, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 60 | 36 | 24 |
Cusp forms | 28 | 20 | 8 |
Eisenstein series | 32 | 16 | 16 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 16 | 4 | 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.ce.a | $2$ | $1.761$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-2}) \) | None | \(2\) | \(-1\) | \(0\) | \(0\) | \(q+q^{2}+\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}^{2}q^{6}+q^{8}+\cdots\) |
3528.1.ce.b | $2$ | $1.761$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-2}) \) | None | \(2\) | \(1\) | \(0\) | \(0\) | \(q+q^{2}-\zeta_{6}^{2}q^{3}+q^{4}-\zeta_{6}^{2}q^{6}+q^{8}+\cdots\) |
3528.1.ce.c | $4$ | $1.761$ | \(\Q(\zeta_{12})\) | $A_{4}$ | None | None | \(0\) | \(4\) | \(0\) | \(0\) | \(q-\zeta_{12}^{3}q^{2}+q^{3}-q^{4}-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{6}+\cdots\) |
3528.1.ce.d | $4$ | $1.761$ | \(\Q(\zeta_{12})\) | $D_{6}$ | \(\Q(\sqrt{-2}) \) | None | \(4\) | \(0\) | \(0\) | \(0\) | \(q+q^{2}+\zeta_{12}^{5}q^{3}+q^{4}+\zeta_{12}^{5}q^{6}+\cdots\) |
3528.1.ce.e | $8$ | $1.761$ | \(\Q(\zeta_{24})\) | $D_{12}$ | \(\Q(\sqrt{-2}) \) | None | \(-8\) | \(0\) | \(0\) | \(0\) | \(q-q^{2}-\zeta_{24}^{7}q^{3}+q^{4}+\zeta_{24}^{7}q^{6}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3528, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3528, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)