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

• Label: 255.2.be
• Level: $255$
• Weight: $2$
• Character orbit: 255.be
• Rep. character: $\chi_{255}(14,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $256$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 255 = 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	255.be (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 255 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(72\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	320	320	0
Cusp forms	256	256	0
Eisenstein series	64	64	0

Trace form

\( 256 q - 32 q^{4} - 16 q^{6} - 16 q^{9} + O(q^{10}) \)

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.be.a	$255$	$2$	255.be	255.ae	$16$	$32$	$4$	$2.036$		\(\Q(\sqrt{-15}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{16}]$
255.2.be.b	$255$	$2$	255.be	255.ae	$16$	$224$	$28$	$2.036$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$