Defining parameters
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.g (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(53\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{20}(21, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 106 | 106 | 0 |
Cusp forms | 98 | 98 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{20}^{\mathrm{new}}(21, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
21.20.g.a | $2$ | $48.052$ | \(\Q(\sqrt{-3}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(59049\) | \(0\) | \(96856453\) | \(q+(3^{9}+3^{9}\zeta_{6})q^{3}+(-2^{19}+2^{19}\zeta_{6})q^{4}+\cdots\) |
21.20.g.b | $96$ | $48.052$ | None | \(0\) | \(-59052\) | \(0\) | \(-38023944\) |