Defining parameters
| Level: | \( N \) | \(=\) | \( 816 = 2^{4} \cdot 3 \cdot 17 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 816.c (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 17 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 6 \) | ||
| Sturm bound: | \(288\) | ||
| Trace bound: | \(13\) | ||
| Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(816, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 156 | 18 | 138 |
| Cusp forms | 132 | 18 | 114 |
| Eisenstein series | 24 | 0 | 24 |
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.c.a | \(2\) | \(6.516\) | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{3}+2iq^{5}+2iq^{7}-q^{9}-6q^{13}+\cdots\) |
| 816.2.c.b | \(2\) | \(6.516\) | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-iq^{3}+3iq^{5}-2iq^{7}-q^{9}+5iq^{11}+\cdots\) |
| 816.2.c.c | \(2\) | \(6.516\) | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{3}-4iq^{7}-q^{9}+4iq^{11}+2q^{13}+\cdots\) |
| 816.2.c.d | \(2\) | \(6.516\) | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-iq^{3}+iq^{5}-2iq^{7}-q^{9}-3iq^{11}+\cdots\) |
| 816.2.c.e | \(4\) | \(6.516\) | \(\Q(i, \sqrt{33})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}-2\beta _{2}q^{7}-q^{9}+\cdots\) |
| 816.2.c.f | \(6\) | \(6.516\) | 6.0.399424.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(816, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(816, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(272, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(408, [\chi])\)\(^{\oplus 2}\)