Defining parameters
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(16\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(21, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 30 | 14 | 16 |
Cusp forms | 22 | 14 | 8 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(21, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
21.6.e.a | $2$ | $3.368$ | \(\Q(\sqrt{-3}) \) | None | \(2\) | \(9\) | \(-11\) | \(259\) | \(q+(2-2\zeta_{6})q^{2}+9\zeta_{6}q^{3}+28\zeta_{6}q^{4}+\cdots\) |
21.6.e.b | $4$ | $3.368$ | \(\Q(\sqrt{-3}, \sqrt{-83})\) | None | \(3\) | \(18\) | \(33\) | \(-350\) | \(q+(1+\beta _{1}-\beta _{3})q^{2}-9\beta _{1}q^{3}+(31\beta _{1}+\cdots)q^{4}+\cdots\) |
21.6.e.c | $8$ | $3.368$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(-3\) | \(-36\) | \(0\) | \(258\) | \(q+(-1+\beta _{1}-\beta _{2})q^{2}+9\beta _{2}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{6}^{\mathrm{old}}(21, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(21, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)