Defining parameters
| Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 256.f (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 16 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(96\) | ||
| Trace bound: | \(13\) | ||
| Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(256, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 152 | 32 | 120 |
| Cusp forms | 104 | 32 | 72 |
| Eisenstein series | 48 | 0 | 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.f.a | $8$ | $6.975$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(-16\) | \(0\) | \(q+\zeta_{24}^{2}q^{3}+(-2-2\zeta_{24}+\zeta_{24}^{4}+\cdots)q^{5}+\cdots\) |
| 256.3.f.b | $8$ | $6.975$ | 8.0.8540717056.1 | None | \(0\) | \(0\) | \(-16\) | \(0\) | \(q+\beta _{2}q^{3}+(-2-2\beta _{1}-\beta _{6})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\) |
| 256.3.f.c | $8$ | $6.975$ | 8.0.8540717056.1 | None | \(0\) | \(0\) | \(16\) | \(0\) | \(q+\beta _{2}q^{3}+(2+2\beta _{1}+\beta _{6})q^{5}+(\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\) |
| 256.3.f.d | $8$ | $6.975$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(16\) | \(0\) | \(q+\zeta_{24}^{2}q^{3}+(2+2\zeta_{24}-\zeta_{24}^{4})q^{5}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(256, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(256, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)