Defining parameters
| Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1800.l (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(360\) | ||
| Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1800, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 60 | 4 | 56 |
| Cusp forms | 12 | 4 | 8 |
| Eisenstein series | 48 | 0 | 48 |
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 \(S_{1}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 1800.1.l.a | $2$ | $0.898$ | \(\Q(\sqrt{-2}) \) | $S_{4}$ | None | None | \(0\) | \(0\) | \(0\) | \(-2\) | \(q-q^{7}-\beta q^{11}+q^{13}+\beta q^{17}+q^{19}+\cdots\) |
| 1800.1.l.b | $2$ | $0.898$ | \(\Q(\sqrt{-2}) \) | $S_{4}$ | None | None | \(0\) | \(0\) | \(0\) | \(2\) | \(q+q^{7}-\beta q^{11}-q^{13}-\beta q^{17}+q^{19}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1800, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)