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

• Label: 455.2.z
• Level: $455$
• Weight: $2$
• Character orbit: 455.z
• Rep. character: $\chi_{455}(186,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $76$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 455 = 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	455.z (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	120	76	44
Cusp forms	104	76	28
Eisenstein series	16	0	16

Trace form

76 * q + 6 * q^3 - 80 * q^4 + 8 * q^7 - 42 * q^9 - 4 * q^10 - 6 * q^11 - 16 * q^12 - 14 * q^14 - 6 * q^15 + 80 * q^16 + 40 * q^17 + 24 * q^18 - 12 * q^19 - 12 * q^20 - 2 * q^21 + 16 * q^22 + 38 * q^25 + 8 * q^26 - 48 * q^27 + 16 * q^28 + 6 * q^29 - 30 * q^31 + 24 * q^33 + 2 * q^35 + 36 * q^36 - 28 * q^38 + 34 * q^39 + 12 * q^40 - 16 * q^42 - 8 * q^43 + 6 * q^44 - 36 * q^47 - 4 * q^48 + 10 * q^49 - 8 * q^51 + 12 * q^52 + 4 * q^53 + 20 * q^55 - 24 * q^56 + 24 * q^60 - 2 * q^61 - 24 * q^62 + 8 * q^63 - 136 * q^64 + 8 * q^65 + 52 * q^66 - 42 * q^67 - 80 * q^68 + 20 * q^69 - 54 * q^71 - 72 * q^72 - 114 * q^73 - 76 * q^74 + 12 * q^75 + 54 * q^76 - 38 * q^77 - 4 * q^78 + 34 * q^79 + 24 * q^80 - 26 * q^81 - 6 * q^82 - 46 * q^84 + 18 * q^85 + 102 * q^86 - 16 * q^87 - 36 * q^88 + 4 * q^90 + 64 * q^91 + 52 * q^92 + 8 * q^95 - 96 * q^97 + 30 * q^98

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.z.a	$455$	$2$	455.z	91.k	$6$	$76$	$38$	$3.633$		None		✓	✓	✓	455.2.z.a	$2$	$0$	\(0\)	\(6\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(455, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)