Defining parameters
| Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 6 \) |
| Character orbit: | \([\chi]\) | \(=\) | 448.e (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 56 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(384\) | ||
| Trace bound: | \(1\) | ||
| Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(448, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 332 | 80 | 252 |
| Cusp forms | 308 | 80 | 228 |
| Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(448, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 448.6.e.a | $8$ | $71.852$ | 8.0.629407744.1 | \(\Q(\sqrt{-14}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-4\beta _{3}-3\beta _{5})q^{3}+(17\beta _{1}-15\beta _{6}+\cdots)q^{5}+\cdots\) |
| 448.6.e.b | $16$ | $71.852$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{8}q^{3}+\beta _{12}q^{5}+(-10\beta _{4}+\beta _{9}+\cdots)q^{7}+\cdots\) |
| 448.6.e.c | $56$ | $71.852$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
Decomposition of \(S_{6}^{\mathrm{old}}(448, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)