Defining parameters
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.g (of order \(8\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 32 \) |
Character field: | \(\Q(\zeta_{8})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(32\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(128, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 80 | 20 | 60 |
Cusp forms | 48 | 12 | 36 |
Eisenstein series | 32 | 8 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(128, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
128.2.g.a | $4$ | $1.022$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(-4\) | \(-4\) | \(q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}-2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\) |
128.2.g.b | $8$ | $1.022$ | 8.0.18939904.2 | None | \(0\) | \(4\) | \(0\) | \(8\) | \(q+(\beta _{2}+\beta _{6}-\beta _{7})q^{3}+(-\beta _{6}-\beta _{7})q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(128, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(128, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)