Defining parameters
| Level: | \( N \) | = | \( 224 = 2^{5} \cdot 7 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Character orbit: | \([\chi]\) | = | 224.f (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | = | \( 28 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(64\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(224, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 40 | 8 | 32 |
| Cusp forms | 24 | 8 | 16 |
| Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(224, [\chi])\) into newform subspaces
| Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
| 224.2.f.a | \(8\) | \(1.789\) | \(\Q(\zeta_{16})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{16}^{2}q^{3}-\zeta_{16}^{5}q^{5}-\zeta_{16}^{6}q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(224, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(224, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)