Space of modular forms of level 276, weight 2, and Character 276.o

• Label: 276.2.o
• Level: $276$
• Weight: $2$
• Character orbit: 276.o
• Rep. character: $\chi_{276}(35,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $440$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.o (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 276 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(276, [\chi])\).

	Total	New	Old
Modular forms	520	520	0
Cusp forms	440	440	0
Eisenstein series	80	80	0

Trace form

\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(276, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
276.2.o.a	$276$	$2$	276.o	276.o	$22$	$440$	$44$	$2.204$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$