Defining parameters
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(128, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 88 | 20 | 68 |
Cusp forms | 72 | 20 | 52 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(128, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
128.6.b.a | $2$ | $20.529$ | \(\Q(\sqrt{-2}) \) | \(\Q(\sqrt{-2}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+11\beta q^{3}-725q^{9}-229\beta q^{11}-1914q^{17}+\cdots\) |
128.6.b.b | $2$ | $20.529$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+19iq^{5}+3^{5}q^{9}+61iq^{13}-2242q^{17}+\cdots\) |
128.6.b.c | $4$ | $20.529$ | \(\Q(i, \sqrt{10})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{3}+21\beta _{1}q^{5}+\beta _{3}q^{7}-397q^{9}+\cdots\) |
128.6.b.d | $4$ | $20.529$ | \(\Q(\sqrt{2}, \sqrt{-29})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{3}-\beta _{3}q^{5}-\beta _{2}q^{7}+11q^{9}+\cdots\) |
128.6.b.e | $4$ | $20.529$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}+3\zeta_{12}^{3}q^{7}+\cdots\) |
128.6.b.f | $4$ | $20.529$ | \(\Q(\sqrt{-2}, \sqrt{-21})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+3\beta _{1}q^{3}+\beta _{3}q^{5}+\beta _{2}q^{7}+171q^{9}+\cdots\) |
Decomposition of \(S_{6}^{\mathrm{old}}(128, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(128, [\chi]) \cong \)