Defining parameters
| Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 256.b (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(64\) | ||
| Trace bound: | \(7\) | ||
| Distinguishing \(T_p\): | \(3\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(256, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 44 | 10 | 34 |
| Cusp forms | 20 | 6 | 14 |
| Eisenstein series | 24 | 4 | 20 |
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.b.a | \(2\) | \(2.044\) | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q+iq^{3}+iq^{5}-4q^{7}-q^{9}+iq^{11}+\cdots\) |
| 256.2.b.b | \(2\) | \(2.044\) | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{5}+3q^{9}+3iq^{13}+2q^{17}+q^{25}+\cdots\) |
| 256.2.b.c | \(2\) | \(2.044\) | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q+iq^{3}-iq^{5}+4q^{7}-q^{9}+iq^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(256, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(256, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)