Defining parameters
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bc (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(128\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(336, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 152 | 36 | 116 |
Cusp forms | 104 | 28 | 76 |
Eisenstein series | 48 | 8 | 40 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(336, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
336.2.bc.a | $2$ | $2.683$ | \(\Q(\sqrt{-3}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(-3\) | \(0\) | \(5\) | \(q+(-1-\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\) |
336.2.bc.b | $2$ | $2.683$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(-3\) | \(-4\) | \(q+(-1+2\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\) |
336.2.bc.c | $2$ | $2.683$ | \(\Q(\sqrt{-3}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(3\) | \(0\) | \(-1\) | \(q+(1+\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\) |
336.2.bc.d | $2$ | $2.683$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(3\) | \(3\) | \(-4\) | \(q+(2-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\) |
336.2.bc.e | $4$ | $2.683$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(10\) | \(q-\zeta_{12}^{2}q^{3}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots\) |
336.2.bc.f | $16$ | $2.683$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q+(-\beta _{5}+\beta _{8})q^{3}-\beta _{14}q^{5}+\beta _{10}q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(336, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)