Defining parameters
| Level: | \( N \) | \(=\) | \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3675.k (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 105 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(560\) | ||
| Trace bound: | \(12\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3675, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 128 | 40 | 88 |
| Cusp forms | 32 | 24 | 8 |
| Eisenstein series | 96 | 16 | 80 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 24 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3675, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 3675.1.k.a | $8$ | $1.834$ | \(\Q(\zeta_{16})\) | $D_{8}$ | \(\Q(\sqrt{-15}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{16}+\zeta_{16}^{3})q^{2}+\zeta_{16}^{2}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots\) |
| 3675.1.k.b | $8$ | $1.834$ | \(\Q(\zeta_{24})\) | $D_{6}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{24}^{9}q^{3}-\zeta_{24}^{6}q^{4}-\zeta_{24}^{6}q^{9}+\cdots\) |
| 3675.1.k.c | $8$ | $1.834$ | \(\Q(\zeta_{16})\) | $D_{8}$ | \(\Q(\sqrt{-15}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{16}+\zeta_{16}^{3})q^{2}-\zeta_{16}^{2}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3675, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3675, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)