Defining parameters
| Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 504.l (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 56 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(96\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(504, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 14 | 5 | 9 |
| Cusp forms | 6 | 3 | 3 |
| Eisenstein series | 8 | 2 | 6 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 3 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(504, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 504.1.l.a | $1$ | $0.252$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) | \(\Q(\sqrt{2}) \) | \(1\) | \(0\) | \(0\) | \(-1\) | \(q+q^{2}+q^{4}-q^{7}+q^{8}-q^{14}+q^{16}+\cdots\) |
| 504.1.l.b | $2$ | $0.252$ | \(\Q(\sqrt{-1}) \) | $D_{2}$ | \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-6}) \) | \(\Q(\sqrt{42}) \) | \(0\) | \(0\) | \(0\) | \(2\) | \(q-i q^{2}-q^{4}+q^{7}+i q^{8}-2 i q^{11}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(504, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(504, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 3}\)