Defining parameters
| Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
| Weight: | \( k \) | \(=\) | \( 9 \) |
| Character orbit: | \([\chi]\) | \(=\) | 192.h (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 24 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(288\) | ||
| Trace bound: | \(9\) | ||
| Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(192, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 268 | 64 | 204 |
| Cusp forms | 244 | 64 | 180 |
| Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(192, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 192.9.h.a | $4$ | $78.217$ | \(\Q(\zeta_{12})\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-3^{4}\zeta_{12}q^{3}+47\zeta_{12}^{3}q^{7}-3^{8}q^{9}+\cdots\) |
| 192.9.h.b | $4$ | $78.217$ | \(\Q(\zeta_{8})\) | \(\Q(\sqrt{-2}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(9\zeta_{8}+\zeta_{8}^{2})q^{3}+(5983+17\zeta_{8}^{3})q^{9}+\cdots\) |
| 192.9.h.c | $16$ | $78.217$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{4}+\beta _{9})q^{3}+\beta _{5}q^{5}+\beta _{6}q^{7}+(-3564+\cdots)q^{9}+\cdots\) |
| 192.9.h.d | $40$ | $78.217$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
Decomposition of \(S_{9}^{\mathrm{old}}(192, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)