Defining parameters
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.v (of order \(8\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 224 \) |
Character field: | \(\Q(\zeta_{8})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(224, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 264 | 264 | 0 |
Cusp forms | 248 | 248 | 0 |
Eisenstein series | 16 | 16 | 0 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(224, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
224.3.v.a | $8$ | $6.104$ | 8.0.157351936.1 | \(\Q(\sqrt{-7}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(2\beta _{6}-\beta _{7})q^{2}+(-\beta _{3}+3\beta _{5})q^{4}+\cdots\) |
224.3.v.b | $240$ | $6.104$ | None | \(-8\) | \(0\) | \(0\) | \(-4\) |