Defining parameters
| Level: | \( N \) | \(=\) | \( 1936 = 2^{4} \cdot 11^{2} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1936.d (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(264\) | ||
| Trace bound: | \(9\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1936, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 47 | 5 | 42 |
| Cusp forms | 11 | 5 | 6 |
| Eisenstein series | 36 | 0 | 36 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 5 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1936, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 1936.1.d.a | $1$ | $0.966$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \) | \(\Q(\sqrt{11}) \) | \(0\) | \(0\) | \(-2\) | \(0\) | \(q-2q^{5}+q^{9}+3q^{25}+2q^{37}-2q^{45}+\cdots\) |
| 1936.1.d.b | $2$ | $0.966$ | \(\Q(\sqrt{-3}) \) | $D_{6}$ | \(\Q(\sqrt{-11}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{5}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{9}+\cdots\) |
| 1936.1.d.c | $2$ | $0.966$ | \(\Q(\sqrt{3}) \) | $D_{6}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q+q^{5}+q^{9}-\beta q^{13}+\beta q^{17}+\beta q^{29}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1936, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1936, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(484, [\chi])\)\(^{\oplus 3}\)