Defining parameters
| Level: | \( N \) | \(=\) | \( 3400 = 2^{3} \cdot 5^{2} \cdot 17 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3400.y (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 136 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(540\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 40 | 22 | 18 |
| Cusp forms | 16 | 10 | 6 |
| Eisenstein series | 24 | 12 | 12 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 10 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3400, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 3400.1.y.a | $2$ | $1.697$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q-i q^{2}+(-i+1)q^{3}-q^{4}+(-i-1)q^{6}+\cdots\) |
| 3400.1.y.b | $4$ | $1.697$ | \(\Q(\zeta_{12})\) | $D_{12}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q-\zeta_{12}^{3}q^{2}+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{3}-q^{4}+\cdots\) |
| 3400.1.y.c | $4$ | $1.697$ | \(\Q(\zeta_{12})\) | $D_{12}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+\zeta_{12}^{3}q^{2}+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-q^{4}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3400, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3400, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 3}\)