Defining parameters
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.x (of order \(8\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 224 \) |
Character field: | \(\Q(\zeta_{8})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(256\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(896, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 544 | 136 | 408 |
Cusp forms | 480 | 120 | 360 |
Eisenstein series | 64 | 16 | 48 |
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.x.a | $8$ | $7.155$ | 8.0.157351936.1 | \(\Q(\sqrt{-7}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{7}-3\beta _{5}q^{9}+(2\beta _{3}+2\beta _{5}-\beta _{6}+\cdots)q^{11}+\cdots\) |
896.2.x.b | $112$ | $7.155$ | None | \(0\) | \(0\) | \(0\) | \(4\) |
Decomposition of \(S_{2}^{\mathrm{old}}(896, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(896, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)