Defining parameters
| Level: | \( N \) | \(=\) | \( 106 = 2 \cdot 53 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 106.b (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 53 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(27\) | ||
| Trace bound: | \(6\) | ||
| Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(106, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 16 | 4 | 12 |
| Cusp forms | 12 | 4 | 8 |
| Eisenstein series | 4 | 0 | 4 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(106, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 106.2.b.a | $2$ | $0.846$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q+i q^{2}+i q^{3}-q^{4}+2 i q^{5}-q^{6}+\cdots\) |
| 106.2.b.b | $2$ | $0.846$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q+i q^{2}-2 i q^{3}-q^{4}-i q^{5}+2 q^{6}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(106, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(106, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(53, [\chi])\)\(^{\oplus 2}\)