Properties

Label 336.2.bl
Level $336$
Weight $2$
Character orbit 336.bl
Rep. character $\chi_{336}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $8$
Sturm bound $128$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(128\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(336, [\chi])\).

Total New Old
Modular forms 152 16 136
Cusp forms 104 16 88
Eisenstein series 48 0 48

Trace form

\( 16 q - 8 q^{9} + O(q^{10}) \) \( 16 q - 8 q^{9} + 8 q^{21} + 20 q^{25} + 36 q^{33} + 4 q^{37} - 56 q^{49} - 24 q^{53} - 8 q^{57} - 72 q^{61} - 24 q^{65} + 12 q^{73} - 8 q^{81} + 96 q^{85} - 28 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(336, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
336.2.bl.a 336.bl 28.f $2$ $2.683$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-6\) \(1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots\)
336.2.bl.b 336.bl 28.f $2$ $2.683$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-3\) \(-5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-3+\cdots)q^{7}+\cdots\)
336.2.bl.c 336.bl 28.f $2$ $2.683$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(3\) \(1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
336.2.bl.d 336.bl 28.f $2$ $2.683$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(6\) \(1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+\cdots\)
336.2.bl.e 336.bl 28.f $2$ $2.683$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-6\) \(-1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
336.2.bl.f 336.bl 28.f $2$ $2.683$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-3\) \(5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
336.2.bl.g 336.bl 28.f $2$ $2.683$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
336.2.bl.h 336.bl 28.f $2$ $2.683$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(6\) \(-1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(-2+3\zeta_{6})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)