Defining parameters
| Level: | \( N \) | \(=\) | \( 2312 = 2^{3} \cdot 17^{2} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2312.j (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 136 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(306\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2312, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 52 | 40 | 12 |
| Cusp forms | 16 | 12 | 4 |
| Eisenstein series | 36 | 28 | 8 |
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 \(S_{1}^{\mathrm{new}}(2312, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 2312.1.j.a | $2$ | $1.154$ | \(\Q(\sqrt{-1}) \) | $D_{2}$ | \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) | \(\Q(\sqrt{17}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{2}-q^{4}-iq^{8}+iq^{9}+q^{16}+\cdots\) |
| 2312.1.j.b | $2$ | $1.154$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+iq^{2}+(1-i)q^{3}-q^{4}+(1+i)q^{6}+\cdots\) |
| 2312.1.j.c | $8$ | $1.154$ | \(\Q(\zeta_{16})\) | $D_{8}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{16}^{4}q^{2}+(\zeta_{16}^{5}-\zeta_{16}^{7})q^{3}-q^{4}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2312, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2312, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 2}\)