Defining parameters
Level: | \( N \) | \(=\) | \( 42 = 2 \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 42.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(42, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 88 | 12 | 76 |
Cusp forms | 72 | 12 | 60 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(42, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
42.6.e.a | $2$ | $6.736$ | \(\Q(\sqrt{-3}) \) | None | \(-4\) | \(-9\) | \(6\) | \(119\) | \(q+(-4+4\zeta_{6})q^{2}-9\zeta_{6}q^{3}-2^{4}\zeta_{6}q^{4}+\cdots\) |
42.6.e.b | $2$ | $6.736$ | \(\Q(\sqrt{-3}) \) | None | \(4\) | \(9\) | \(-86\) | \(49\) | \(q+(4-4\zeta_{6})q^{2}+9\zeta_{6}q^{3}-2^{4}\zeta_{6}q^{4}+\cdots\) |
42.6.e.c | $4$ | $6.736$ | \(\Q(\sqrt{-3}, \sqrt{9601})\) | None | \(-8\) | \(18\) | \(53\) | \(6\) | \(q-4\beta _{2}q^{2}+(9-9\beta _{2})q^{3}+(-2^{4}+2^{4}\beta _{2}+\cdots)q^{4}+\cdots\) |
42.6.e.d | $4$ | $6.736$ | \(\Q(\sqrt{-3}, \sqrt{505})\) | None | \(8\) | \(-18\) | \(-17\) | \(-408\) | \(q+(4-4\beta _{1})q^{2}-9\beta _{1}q^{3}-2^{4}\beta _{1}q^{4}+\cdots\) |
Decomposition of \(S_{6}^{\mathrm{old}}(42, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(42, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)