Defining parameters
| Level: | \( N \) | \(=\) | \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3800.bn (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 760 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(600\) | ||
| Trace bound: | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3800, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 44 | 20 | 24 |
| Cusp forms | 20 | 12 | 8 |
| Eisenstein series | 24 | 8 | 16 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 12 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3800, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 3800.1.bn.a | $4$ | $1.896$ | \(\Q(\zeta_{12})\) | $D_{3}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\) |
| 3800.1.bn.b | $4$ | $1.896$ | \(\Q(\zeta_{12})\) | $D_{3}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\) |
| 3800.1.bn.c | $4$ | $1.896$ | \(\Q(\zeta_{12})\) | $D_{3}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3800, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3800, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 2}\)