Space of modular forms of level 684, weight 2, and Character 684.n

• Label: 684.2.n
• Level: $684$
• Weight: $2$
• Character orbit: 684.n
• Rep. character: $\chi_{684}(65,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $40$
• Newform subspaces: $2$
• Sturm bound: $240$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 171 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(240\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(684, [\chi])\).

	Total	New	Old
Modular forms	252	40	212
Cusp forms	228	40	188
Eisenstein series	24	0	24

Trace form

\( 40 q + 3 q^{3} + q^{7} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(684, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
684.2.n.a	$684$	$2$	684.n	171.k	$6$	$2$	$1$	$5.462$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{7}-3q^{9}+\cdots\)
684.2.n.b	$684$	$2$	684.n	171.k	$6$	$38$	$19$	$5.462$		None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(2\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(684, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(684, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)