Defining parameters
| Level: | \( N \) | \(=\) | \( 2775 = 3 \cdot 5^{2} \cdot 37 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2775.b (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 555 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(380\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2775, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 34 | 10 | 24 |
| Cusp forms | 22 | 6 | 16 |
| Eisenstein series | 12 | 4 | 8 |
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 \(S_{1}^{\mathrm{new}}(2775, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 2775.1.b.a | $2$ | $1.385$ | \(\Q(\sqrt{-1}) \) | $D_{2}$ | \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-111}) \) | \(\Q(\sqrt{37}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-i q^{3}+q^{4}-2 i q^{7}-q^{9}-i q^{12}+\cdots\) |
| 2775.1.b.b | $4$ | $1.385$ | \(\Q(\zeta_{8})\) | $D_{4}$ | \(\Q(\sqrt{-111}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2775, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2775, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)