Defining parameters
| Level: | \( N \) | = | \( 448 = 2^{6} \cdot 7 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Character orbit: | \([\chi]\) | = | 448.f (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | = | \( 28 \) |
| Character field: | \(\Q\) | ||
| Newforms: | \( 4 \) | ||
| Sturm bound: | \(128\) | ||
| Trace bound: | \(3\) | ||
| Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(448, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 76 | 18 | 58 |
| Cusp forms | 52 | 14 | 38 |
| Eisenstein series | 24 | 4 | 20 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(448, [\chi])\) into irreducible Hecke orbits
| Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
| 448.2.f.a | \(2\) | \(3.577\) | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-4\) | \(0\) | \(-4\) | \(q-2q^{3}-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+q^{9}+\cdots\) |
| 448.2.f.b | \(2\) | \(3.577\) | \(\Q(\sqrt{-7}) \) | \(\Q(\sqrt{-7}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta q^{7}-3q^{9}-2\beta q^{11}-2\beta q^{23}+\cdots\) |
| 448.2.f.c | \(2\) | \(3.577\) | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(4\) | \(0\) | \(4\) | \(q+2q^{3}+2\zeta_{6}q^{5}+(2-\zeta_{6})q^{7}+q^{9}+\cdots\) |
| 448.2.f.d | \(8\) | \(3.577\) | \(\Q(\zeta_{16})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{16}^{2}q^{3}-\zeta_{16}^{5}q^{5}-\zeta_{16}^{4}q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(448, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)