Defining parameters
| Level: | \( N \) | \(=\) | \( 96 = 2^{5} \cdot 3 \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 96.h (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 24 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(48\) | ||
| Trace bound: | \(3\) | ||
| Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(96, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 40 | 10 | 30 |
| Cusp forms | 24 | 6 | 18 |
| Eisenstein series | 16 | 4 | 12 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(96, [\chi])\) into newform subspaces
| Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
| 96.3.h.a | \(1\) | \(2.616\) | \(\Q\) | \(\Q(\sqrt{-6}) \) | \(0\) | \(-3\) | \(2\) | \(10\) | \(q-3q^{3}+2q^{5}+10q^{7}+9q^{9}+10q^{11}+\cdots\) |
| 96.3.h.b | \(1\) | \(2.616\) | \(\Q\) | \(\Q(\sqrt{-6}) \) | \(0\) | \(3\) | \(-2\) | \(10\) | \(q+3q^{3}-2q^{5}+10q^{7}+9q^{9}-10q^{11}+\cdots\) |
| 96.3.h.c | \(4\) | \(2.616\) | \(\Q(\sqrt{2}, \sqrt{-7})\) | None | \(0\) | \(0\) | \(0\) | \(-16\) | \(q+(-\beta _{1}-\beta _{2})q^{3}-2\beta _{1}q^{5}-4q^{7}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(96, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(96, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)