Defining parameters
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 84 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(336\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1764, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 48 | 8 | 40 |
Cusp forms | 16 | 8 | 8 |
Eisenstein series | 32 | 0 | 32 |
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 \(S_{1}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1764.1.h.a | $8$ | $0.880$ | \(\Q(\zeta_{16})\) | $D_{8}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{16}^{4}q^{2}-q^{4}+(\zeta_{16}^{3}-\zeta_{16}^{5})q^{5}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)