Defining parameters
| Level: | \( N \) | \(=\) | \( 816 = 2^{4} \cdot 3 \cdot 17 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 816.bf (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 204 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 5 \) | ||
| Sturm bound: | \(288\) | ||
| Trace bound: | \(13\) | ||
| Distinguishing \(T_p\): | \(5\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(816, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 312 | 72 | 240 |
| Cusp forms | 264 | 72 | 192 |
| Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(816, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 816.2.bf.a | $8$ | $6.516$ | 8.0.12960000.1 | None | \(0\) | \(-4\) | \(0\) | \(0\) | \(q+(-\beta _{2}+\beta _{5})q^{3}+\beta _{4}q^{5}+\beta _{3}q^{7}+\cdots\) |
| 816.2.bf.b | $8$ | $6.516$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{24}^{7}q^{3}+\zeta_{24}q^{5}+(-\zeta_{24}^{4}+\zeta_{24}^{6}+\cdots)q^{7}+\cdots\) |
| 816.2.bf.c | $8$ | $6.516$ | 8.0.12960000.1 | None | \(0\) | \(4\) | \(0\) | \(0\) | \(q+(1-\beta _{1}+\beta _{5})q^{3}+\beta _{3}q^{5}-\beta _{4}q^{7}+\cdots\) |
| 816.2.bf.d | $24$ | $6.516$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
| 816.2.bf.e | $24$ | $6.516$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
Decomposition of \(S_{2}^{\mathrm{old}}(816, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(816, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(408, [\chi])\)\(^{\oplus 2}\)