Defining parameters
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.g (of order \(8\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 32 \) |
Character field: | \(\Q(\zeta_{8})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(64\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(256, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 160 | 40 | 120 |
Cusp forms | 96 | 24 | 72 |
Eisenstein series | 64 | 16 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(256, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
256.2.g.a | $4$ | $2.044$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(4\) | \(-4\) | \(q+(\zeta_{8}+\zeta_{8}^{2})q^{3}+(1+\zeta_{8}+2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{5}+\cdots\) |
256.2.g.b | $4$ | $2.044$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(4\) | \(4\) | \(q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(1+\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\) |
256.2.g.c | $8$ | $2.044$ | 8.0.18939904.2 | None | \(0\) | \(-4\) | \(0\) | \(8\) | \(q+(-1+\beta _{1}+\beta _{6}-\beta _{7})q^{3}+(\beta _{4}-\beta _{7})q^{5}+\cdots\) |
256.2.g.d | $8$ | $2.044$ | 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 \(S_{2}^{\mathrm{old}}(256, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(256, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)