Defining parameters
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(8\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(21, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 8 | 2 | 6 |
Cusp forms | 4 | 2 | 2 |
Eisenstein series | 4 | 0 | 4 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(21, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
21.3.d.a | $2$ | $0.572$ | \(\Q(\sqrt{-3}) \) | None | \(2\) | \(0\) | \(0\) | \(2\) | \(q+q^{2}+\zeta_{6}q^{3}-3q^{4}-4\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(21, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(21, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)