Defining parameters
| Level: | \( N \) | \(=\) | \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2700.c (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(540\) | ||
| Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2700, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 44 | 4 | 40 |
| Cusp forms | 8 | 4 | 4 |
| Eisenstein series | 36 | 0 | 36 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2700, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 2700.1.c.a | $2$ | $1.347$ | \(\Q(\sqrt{-3}) \) | $D_{6}$ | \(\Q(\sqrt{-15}) \) | None | \(-1\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}+\zeta_{6}^{2}q^{16}+\cdots\) |
| 2700.1.c.b | $2$ | $1.347$ | \(\Q(\sqrt{-3}) \) | $D_{6}$ | \(\Q(\sqrt{-15}) \) | None | \(1\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{16}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2700, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2700, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)