Defining parameters
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
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: | \(32\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(21, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 62 | 30 | 32 |
Cusp forms | 54 | 30 | 24 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(21, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
21.12.e.a | $14$ | $16.135$ | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) | None | \(9\) | \(-1701\) | \(7218\) | \(9219\) | \(q+(1+\beta _{1}+\beta _{2})q^{2}+3^{5}\beta _{2}q^{3}+(1241\beta _{2}+\cdots)q^{4}+\cdots\) |
21.12.e.b | $16$ | $16.135$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(-55\) | \(1944\) | \(-2156\) | \(-6560\) | \(q+(-7-7\beta _{2}-\beta _{4})q^{2}-3^{5}\beta _{2}q^{3}+\cdots\) |
Decomposition of \(S_{12}^{\mathrm{old}}(21, [\chi])\) into lower level spaces
\( S_{12}^{\mathrm{old}}(21, [\chi]) \cong \) \(S_{12}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)