Defining parameters
Level: | \( N \) | \(=\) | \( 266 = 2 \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 266.f (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(80\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(266, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 88 | 20 | 68 |
Cusp forms | 72 | 20 | 52 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(266, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
266.2.f.a | $2$ | $2.124$ | \(\Q(\sqrt{-3}) \) | None | \(-1\) | \(0\) | \(-1\) | \(2\) | \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\) |
266.2.f.b | $4$ | $2.124$ | \(\Q(\sqrt{-3}, \sqrt{17})\) | None | \(2\) | \(-1\) | \(1\) | \(-4\) | \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\) |
266.2.f.c | $6$ | $2.124$ | 6.0.591408.1 | None | \(-3\) | \(-2\) | \(1\) | \(-6\) | \(q-\beta _{4}q^{2}+(\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots\) |
266.2.f.d | $8$ | $2.124$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(4\) | \(1\) | \(-1\) | \(8\) | \(q+(1-\beta _{4})q^{2}+(-\beta _{1}-\beta _{3})q^{3}-\beta _{4}q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(266, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(266, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 2}\)