Defining parameters
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.c (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(12\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(14, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 24 | 8 | 16 |
Cusp forms | 16 | 8 | 8 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(14, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
14.6.c.a | $4$ | $2.245$ | \(\Q(\sqrt{-3}, \sqrt{79})\) | None | \(-8\) | \(-14\) | \(-70\) | \(0\) | \(q+4\beta _{2}q^{2}+(-7-\beta _{1}-7\beta _{2})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\) |
14.6.c.b | $4$ | $2.245$ | \(\Q(\sqrt{-3}, \sqrt{130})\) | None | \(8\) | \(14\) | \(42\) | \(232\) | \(q-4\beta _{2}q^{2}+(7-\beta _{1}+7\beta _{2})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{6}^{\mathrm{old}}(14, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(14, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)