Defining parameters
| Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 63.c (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(32\) | ||
| Trace bound: | \(4\) | ||
| Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(63, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 28 | 8 | 20 |
| Cusp forms | 20 | 8 | 12 |
| Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(63, [\chi])\) into newform subspaces
| Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
| 63.4.c.a | \(4\) | \(3.717\) | \(\Q(\sqrt{-2}, \sqrt{7})\) | \(\Q(\sqrt{-7}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{2}+(-8-5\beta _{3})q^{4}-7\beta _{3}q^{7}+\cdots\) |
| 63.4.c.b | \(4\) | \(3.717\) | \(\Q(\sqrt{-2}, \sqrt{111})\) | None | \(0\) | \(0\) | \(0\) | \(-44\) | \(q+2\beta _{1}q^{2}+\beta _{3}q^{5}+(-11-\beta _{2})q^{7}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(63, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(63, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)