Defining parameters
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.bf (of order \(18\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 540 \) |
Character field: | \(\Q(\zeta_{18})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(324\) | ||
Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1620, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 108 | 36 | 72 |
Cusp forms | 36 | 12 | 24 |
Eisenstein series | 72 | 24 | 48 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 12 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1620, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1620.1.bf.a | $6$ | $0.808$ | \(\Q(\zeta_{18})\) | $D_{9}$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(0\) | \(0\) | \(-3\) | \(q-\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+\zeta_{18}q^{5}+(\zeta_{18}^{4}+\cdots)q^{7}+\cdots\) |
1620.1.bf.b | $6$ | $0.808$ | \(\Q(\zeta_{18})\) | $D_{9}$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(0\) | \(0\) | \(3\) | \(q+\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+\zeta_{18}q^{5}+(-\zeta_{18}^{4}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1620, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)