Space of modular forms of level 268, weight 2, and Character 268.n

• Label: 268.2.n
• Level: $268$
• Weight: $2$
• Character orbit: 268.n
• Rep. character: $\chi_{268}(7,\cdot)$
• Character field: $\Q(\zeta_{66})$
• Dimension: $640$
• Newform subspaces: $1$
• Sturm bound: $68$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 268 = 2^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	268.n (of order \(66\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 268 \)
Character field:			\(\Q(\zeta_{66})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(68\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(268, [\chi])\).

	Total	New	Old
Modular forms	720	720	0
Cusp forms	640	640	0
Eisenstein series	80	80	0

Trace form

\( 640 q - 19 q^{2} - 23 q^{4} - 44 q^{5} - 19 q^{6} + 11 q^{8} - 88 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(268, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
268.2.n.a	$268$	$2$	268.n	268.n	$66$	$640$	$32$	$2.140$		None		$4$	$0$	\(-19\)	\(0\)	\(-44\)	\(0\)		$\mathrm{SU}(2)[C_{66}]$