Defining parameters
| Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 800.p (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(120\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(800, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 58 | 6 | 52 |
| Cusp forms | 10 | 6 | 4 |
| 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 | 6 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(800, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 800.1.p.a | $2$ | $0.399$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(-2\) | \(0\) | \(2\) | \(q+(-1+i)q^{3}+(1+i)q^{7}-iq^{9}-q^{21}+\cdots\) |
| 800.1.p.b | $2$ | $0.399$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{9}+(1-i)q^{13}+(1+i)q^{17}+(-1+\cdots)q^{37}+\cdots\) |
| 800.1.p.c | $2$ | $0.399$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(2\) | \(0\) | \(-2\) | \(q+(1-i)q^{3}+(-1-i)q^{7}-iq^{9}-q^{21}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(800, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)