Defining parameters
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
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: | \(37\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{14}(21, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 74 | 74 | 0 |
Cusp forms | 66 | 66 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{14}^{\mathrm{new}}(21, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
21.14.g.a | $2$ | $22.518$ | \(\Q(\sqrt{-3}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(-2187\) | \(0\) | \(386569\) | \(q+(-3^{6}-3^{6}\zeta_{6})q^{3}+(-2^{13}+2^{13}\zeta_{6})q^{4}+\cdots\) |
21.14.g.b | $64$ | $22.518$ | None | \(0\) | \(2184\) | \(0\) | \(-666904\) |