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

• Label: 276.2.g
• Level: $276$
• Weight: $2$
• Character orbit: 276.g
• Rep. character: $\chi_{276}(137,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• 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.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 69 \)
Character field:			\(\Q\)
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	54	8	46
Cusp forms	42	8	34
Eisenstein series	12	0	12

Trace form

\( 8 q + 2 q^{3} - 6 q^{9} + O(q^{10}) \)

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.g.a	$276$	$2$	276.g	69.c	$2$	$8$	$8$	$2.204$	8.0.\(\cdots\).7	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+\beta _{5}q^{5}-\beta _{7}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(276, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(276, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)