Defining parameters
Level: | \( N \) | \(=\) | \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3528.cu (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
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 | 180 | 4 | 176 |
Cusp forms | 52 | 4 | 48 |
Eisenstein series | 128 | 0 | 128 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 0 | 0 | 4 | 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.cu.a | $4$ | $1.761$ | \(\Q(\sqrt{-2}, \sqrt{-3})\) | $S_{4}$ | None | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\beta _{1}+\beta _{3})q^{5}-\beta _{1}q^{11}+q^{13}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3528, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3528, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 4}\)