Defining parameters
| Level: | \( N \) | \(=\) | \( 3136 = 2^{6} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3136.r (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(448\) | ||
| Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3136, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 160 | 18 | 142 |
| Cusp forms | 64 | 10 | 54 |
| Eisenstein series | 96 | 8 | 88 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 6 | 4 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3136, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 3136.1.r.a | $2$ | $1.565$ | \(\Q(\sqrt{-3}) \) | $D_{2}$ | \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) | \(\Q(\sqrt{7}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{25}+q^{29}-\zeta_{6}q^{37}+\cdots\) |
| 3136.1.r.b | $4$ | $1.565$ | \(\Q(\zeta_{12})\) | $A_{4}$ | None | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{5}q^{11}+\cdots\) |
| 3136.1.r.c | $4$ | $1.565$ | \(\Q(\sqrt{2}, \sqrt{-3})\) | $D_{4}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{1}+\beta _{3})q^{5}+\beta _{2}q^{9}+\beta _{3}q^{13}-\beta _{1}q^{17}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3136, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3136, [\chi]) \cong \)