Space of modular forms of level 277, weight 2, and Character 277.i

• Label: 277.2.i
• Level: $277$
• Weight: $2$
• Character orbit: 277.i
• Rep. character: $\chi_{277}(3,\cdot)$
• Character field: $\Q(\zeta_{69})$
• Dimension: $968$
• Newform subspaces: $1$
• Sturm bound: $46$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	277.i (of order \(69\) and degree \(44\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 277 \)
Character field:			\(\Q(\zeta_{69})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(46\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(277, [\chi])\).

	Total	New	Old
Modular forms	1056	1056	0
Cusp forms	968	968	0
Eisenstein series	88	88	0

Trace form

\( 968 q - 42 q^{2} - 46 q^{3} - 86 q^{4} - 48 q^{5} - 40 q^{6} - 44 q^{7} - 34 q^{8} - 26 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(277, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
277.2.i.a	$277$	$2$	277.i	277.i	$69$	$968$	$22$	$2.212$		None		$2$	$0$	\(-42\)	\(-46\)	\(-48\)	\(-44\)		$\mathrm{SU}(2)[C_{69}]$