Space of modular forms of level 336, weight 2, and Character 336.bl

• 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: $5$

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

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

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
336.2.bl.a	$336$	$2$	336.bl	28.f	$6$	$2$	$1$	$2.683$	\(\Q(\sqrt{-3}) \)	None		✓			336.2.bl.a	$2$	$1$	\(0\)	\(-1\)	\(-6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots\)
336.2.bl.b	$336$	$2$	336.bl	28.f	$6$	$2$	$1$	$2.683$	\(\Q(\sqrt{-3}) \)	None		✓			336.2.bl.b	$2$	$1$	\(0\)	\(-1\)	\(-3\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-3+\cdots)q^{7}+\cdots\)
336.2.bl.c	$336$	$2$	336.bl	28.f	$6$	$2$	$1$	$2.683$	\(\Q(\sqrt{-3}) \)	None		✓			336.2.bl.c	$2$	$0$	\(0\)	\(-1\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
336.2.bl.d	$336$	$2$	336.bl	28.f	$6$	$2$	$1$	$2.683$	\(\Q(\sqrt{-3}) \)	None		✓			336.2.bl.d	$2$	$0$	\(0\)	\(-1\)	\(6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+\cdots\)
336.2.bl.e	$336$	$2$	336.bl	28.f	$6$	$2$	$1$	$2.683$	\(\Q(\sqrt{-3}) \)	None		✓			336.2.bl.a	$2$	$0$	\(0\)	\(1\)	\(-6\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
336.2.bl.f	$336$	$2$	336.bl	28.f	$6$	$2$	$1$	$2.683$	\(\Q(\sqrt{-3}) \)	None		✓			336.2.bl.b	$2$	$0$	\(0\)	\(1\)	\(-3\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
336.2.bl.g	$336$	$2$	336.bl	28.f	$6$	$2$	$1$	$2.683$	\(\Q(\sqrt{-3}) \)	None		✓			336.2.bl.c	$2$	$0$	\(0\)	\(1\)	\(3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
336.2.bl.h	$336$	$2$	336.bl	28.f	$6$	$2$	$1$	$2.683$	\(\Q(\sqrt{-3}) \)	None		✓			336.2.bl.d	$2$	$0$	\(0\)	\(1\)	\(6\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(-2+3\zeta_{6})q^{7}+\cdots\)

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

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