Space of modular forms of level 455, weight 2, and Character 455.bj

• Label: 455.2.bj
• Level: $455$
• Weight: $2$
• Character orbit: 455.bj
• Rep. character: $\chi_{455}(134,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $88$
• Newform subspaces: $2$
• Sturm bound: $112$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 455 = 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	455.bj (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(112\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(455, [\chi])\).

	Total	New	Old
Modular forms	120	88	32
Cusp forms	104	88	16
Eisenstein series	16	0	16

Trace form

88 * q - 48 * q^4 + 54 * q^9 + 2 * q^10 - 16 * q^14 - 12 * q^15 - 40 * q^16 - 30 * q^20 - 48 * q^24 - 12 * q^25 + 36 * q^26 + 2 * q^29 + 16 * q^30 + 2 * q^35 + 64 * q^36 - 26 * q^39 + 40 * q^40 - 48 * q^41 + 30 * q^45 + 24 * q^46 - 44 * q^49 - 36 * q^50 - 96 * q^51 - 84 * q^54 + 30 * q^55 + 24 * q^56 + 60 * q^59 - 36 * q^61 + 128 * q^64 - 20 * q^65 - 80 * q^66 - 16 * q^69 - 12 * q^71 + 84 * q^74 - 26 * q^75 + 60 * q^76 - 52 * q^79 + 66 * q^80 - 56 * q^81 + 24 * q^84 - 60 * q^85 + 12 * q^89 - 124 * q^90 + 6 * q^91 - 72 * q^94 - 10 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(455, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
455.2.bj.a	$455$	$2$	455.bj	65.l	$6$	$44$	$22$	$3.633$		None		✓			455.2.bj.a	$2$	$0$	\(-4\)	\(3\)	\(2\)	\(22\)		$\mathrm{SU}(2)[C_{6}]$
455.2.bj.b	$455$	$2$	455.bj	65.l	$6$	$44$	$22$	$3.633$		None		✓			455.2.bj.a	$2$	$0$	\(4\)	\(-3\)	\(-2\)	\(-22\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(455, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(455, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)