Defining parameters
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(10\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(21, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 8 | 12 |
Cusp forms | 12 | 8 | 4 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(21, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
21.4.e.a | $2$ | $1.239$ | \(\Q(\sqrt{-3}) \) | None | \(3\) | \(-3\) | \(3\) | \(-7\) | \(q+(3-3\zeta_{6})q^{2}-3\zeta_{6}q^{3}-\zeta_{6}q^{4}+(3+\cdots)q^{5}+\cdots\) |
21.4.e.b | $6$ | $1.239$ | 6.0.9924270768.1 | None | \(-1\) | \(9\) | \(-11\) | \(-13\) | \(q-\beta _{1}q^{2}+(3-3\beta _{4})q^{3}+(-8+\beta _{1}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(21, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(21, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)