Defining parameters
| Level: | \( N \) | \(=\) | \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3332.m (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 68 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(504\) | ||
| Trace bound: | \(10\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3332, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 44 | 26 | 18 |
| Cusp forms | 12 | 6 | 6 |
| Eisenstein series | 32 | 20 | 12 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 6 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3332, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 3332.1.m.a | $2$ | $1.663$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q-iq^{2}-q^{4}+(-1-i)q^{5}+iq^{8}+\cdots\) |
| 3332.1.m.b | $2$ | $1.663$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q+iq^{2}-q^{4}+(1+i)q^{5}-iq^{8}+iq^{9}+\cdots\) |
| 3332.1.m.c | $2$ | $1.663$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q-iq^{2}-q^{4}+(1+i)q^{5}+iq^{8}+iq^{9}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3332, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3332, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 3}\)