Defining parameters
| Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 896.f (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(256\) | ||
| Trace bound: | \(21\) | ||
| Distinguishing \(T_p\): | \(3\), \(29\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(896, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 144 | 32 | 112 |
| Cusp forms | 112 | 32 | 80 |
| Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(896, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 896.2.f.a | $8$ | $7.155$ | 8.0.40960000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{6}q^{3}+\beta _{1}q^{5}+(\beta _{4}+\beta _{7})q^{7}+\beta _{2}q^{9}+\cdots\) |
| 896.2.f.b | $8$ | $7.155$ | 8.0.40960000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{6}q^{3}-\beta _{1}q^{5}+(-\beta _{4}-\beta _{7})q^{7}+\cdots\) |
| 896.2.f.c | $8$ | $7.155$ | 8.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+(-\beta _{2}+\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\) |
| 896.2.f.d | $8$ | $7.155$ | 8.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{3}-\beta _{1}q^{5}+(\beta _{2}-\beta _{4}-\beta _{5})q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(896, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(896, [\chi]) \cong \)