Defining parameters
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.g (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
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 | 30 | 0 |
Cusp forms | 22 | 22 | 0 |
Eisenstein series | 8 | 8 | 0 |
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.g.a | $2$ | $3.368$ | \(\Q(\sqrt{-3}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(27\) | \(0\) | \(211\) | \(q+(9+9\zeta_{6})q^{3}+(-2^{5}+2^{5}\zeta_{6})q^{4}+\cdots\) |
21.6.g.b | $4$ | $3.368$ | \(\Q(\sqrt{-3}, \sqrt{-17})\) | None | \(0\) | \(-48\) | \(0\) | \(490\) | \(q+2\beta _{1}q^{2}+(-2^{4}+\beta _{1}+8\beta _{2}+\beta _{3})q^{3}+\cdots\) |
21.6.g.c | $16$ | $3.368$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(18\) | \(0\) | \(-616\) | \(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{6})q^{3}+(12+\cdots)q^{4}+\cdots\) |