Space of modular forms of level 255, weight 2, and Character 255.v

• Label: 255.2.v
• Level: $255$
• Weight: $2$
• Character orbit: 255.v
• Rep. character: $\chi_{255}(53,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $128$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 255 = 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	255.v (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 255 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(255, [\chi])\).

	Total	New	Old
Modular forms	160	160	0
Cusp forms	128	128	0
Eisenstein series	32	32	0

Trace form

\( 128 q - 4 q^{3} - 112 q^{4} - 8 q^{6} - 8 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(255, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
255.2.v.a	$255$	$2$	255.v	255.v	$8$	$128$	$32$	$2.036$		None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{8}]$