Defining parameters
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.h (of order \(8\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 32 \) |
Character field: | \(\Q(\zeta_{8})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(256, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 288 | 72 | 216 |
Cusp forms | 224 | 56 | 168 |
Eisenstein series | 64 | 16 | 48 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(256, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
256.3.h.a | $28$ | $6.975$ | None | \(0\) | \(-4\) | \(4\) | \(4\) | ||
256.3.h.b | $28$ | $6.975$ | None | \(0\) | \(4\) | \(4\) | \(-4\) |
Decomposition of \(S_{3}^{\mathrm{old}}(256, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(256, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)