Defining parameters
| Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1216.e (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(160\) | ||
| Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1216, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 22 | 4 | 18 |
| Cusp forms | 10 | 2 | 8 |
| Eisenstein series | 12 | 2 | 10 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 2 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1216, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 1216.1.e.a | $1$ | $0.607$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-19}) \) | None | \(0\) | \(0\) | \(1\) | \(-1\) | \(q+q^{5}-q^{7}+q^{9}+q^{11}-q^{17}-q^{19}+\cdots\) |
| 1216.1.e.b | $1$ | $0.607$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-19}) \) | None | \(0\) | \(0\) | \(1\) | \(1\) | \(q+q^{5}+q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1216, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1216, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)