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

• Label: 255.2.w
• Level: $255$
• Weight: $2$
• Character orbit: 255.w
• Rep. character: $\chi_{255}(76,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $48$
• 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.w (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{8})\)
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	160	48	112
Cusp forms	128	48	80
Eisenstein series	32	0	32

Trace form

48 * q + 8 * q^6 - 48 * q^16 + 16 * q^17 + 16 * q^22 - 16 * q^23 - 8 * q^24 - 32 * q^26 - 48 * q^28 + 16 * q^29 - 32 * q^33 + 8 * q^34 - 8 * q^36 - 16 * q^37 - 16 * q^39 - 16 * q^40 + 16 * q^41 - 16 * q^42 + 16 * q^43 + 32 * q^44 - 32 * q^46 + 16 * q^49 + 96 * q^52 + 16 * q^53 + 8 * q^54 + 32 * q^56 + 64 * q^58 - 48 * q^59 + 8 * q^60 - 80 * q^61 - 32 * q^62 + 16 * q^66 - 32 * q^67 + 80 * q^68 - 16 * q^71 - 96 * q^74 - 16 * q^76 - 96 * q^77 + 48 * q^78 - 16 * q^79 + 64 * q^80 + 16 * q^82 + 48 * q^83 + 48 * q^84 + 32 * q^86 - 64 * q^88 + 64 * q^91 + 64 * q^92 - 56 * q^94 + 64 * q^96 - 32 * q^97

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
255.2.w.a	$255$	$2$	255.w	17.d	$8$	$16$	$4$	$2.036$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			255.2.w.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-\beta _{2}-\beta _{5}-\beta _{7}-\beta _{8}-\beta _{10}+\beta _{13}+\cdots)q^{2}+\cdots\)
255.2.w.b	$255$	$2$	255.w	17.d	$8$	$32$	$8$	$2.036$		None		✓	✓		255.2.w.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(255, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(255, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)