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

• Label: 255.2.g
• Level: $255$
• Weight: $2$
• Character orbit: 255.g
• Rep. character: $\chi_{255}(16,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• 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.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
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	40	12	28
Cusp forms	32	12	20
Eisenstein series	8	0	8

Trace form

12 * q + 16 * q^4 - 12 * q^9 - 16 * q^13 + 4 * q^15 + 32 * q^16 - 8 * q^17 - 16 * q^19 - 12 * q^25 + 24 * q^26 - 4 * q^30 - 80 * q^32 + 12 * q^34 + 8 * q^35 - 16 * q^36 + 16 * q^38 - 32 * q^42 - 8 * q^43 + 32 * q^47 - 4 * q^49 + 12 * q^51 - 8 * q^52 + 48 * q^53 - 16 * q^55 + 8 * q^59 + 4 * q^60 + 20 * q^64 + 36 * q^66 - 32 * q^67 + 8 * q^68 + 8 * q^69 + 36 * q^70 - 116 * q^76 + 12 * q^81 + 16 * q^83 + 36 * q^84 + 4 * q^85 - 64 * q^86 + 32 * q^87 + 16 * q^89 + 8 * q^93 + 4 * q^94 + 16 * q^98

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.g.a	$255$	$2$	255.g	17.b	$2$	$4$	$4$	$2.036$	\(\Q(i, \sqrt{13})\)	None		✓			255.2.g.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{3})q^{2}-\beta _{2}q^{3}+(2-\beta _{3})q^{4}+\cdots\)
255.2.g.b	$255$	$2$	255.g	17.b	$2$	$8$	$8$	$2.036$	8.0.\(\cdots\).1	None		✓	✓		255.2.g.b	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{5}q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+\cdots\)

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

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