Defining parameters
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.h (of order \(8\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 32 \) |
Character field: | \(\Q(\zeta_{8})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(128, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 144 | 36 | 108 |
Cusp forms | 112 | 28 | 84 |
Eisenstein series | 32 | 8 | 24 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(128, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
128.3.h.a | $28$ | $3.488$ | None | \(0\) | \(4\) | \(-4\) | \(4\) |
Decomposition of \(S_{3}^{\mathrm{old}}(128, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(128, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)