Space of modular forms of level 85, weight 4, and Character 85.r

• Label: 85.4.r
• Level: $85$
• Weight: $4$
• Character orbit: 85.r
• Rep. character: $\chi_{85}(12,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $200$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	85.r (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(85, [\chi])\).

	Total	New	Old
Modular forms	232	232	0
Cusp forms	200	200	0
Eisenstein series	32	32	0

Trace form

200 * q - 8 * q^2 - 8 * q^3 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 72 * q^8 - 24 * q^10 - 16 * q^11 + 208 * q^12 - 16 * q^13 + 416 * q^14 - 344 * q^15 - 8 * q^17 - 16 * q^18 - 96 * q^19 - 648 * q^20 - 16 * q^21 - 8 * q^22 - 8 * q^23 + 440 * q^25 + 720 * q^26 + 1096 * q^27 - 264 * q^28 - 1352 * q^30 - 880 * q^31 + 568 * q^32 - 768 * q^33 + 576 * q^34 - 16 * q^35 - 1744 * q^36 + 856 * q^37 - 1648 * q^39 + 1728 * q^40 + 904 * q^41 + 984 * q^42 - 8 * q^43 - 8 * q^45 + 1952 * q^46 - 5192 * q^48 + 448 * q^50 - 16 * q^51 - 3088 * q^52 + 3040 * q^53 - 1728 * q^54 + 2840 * q^55 - 16 * q^56 - 1864 * q^57 + 1280 * q^58 - 3200 * q^59 + 5432 * q^60 - 16 * q^61 + 3928 * q^62 - 4304 * q^63 + 4224 * q^64 - 1008 * q^65 - 16 * q^66 + 192 * q^67 - 11792 * q^68 + 2296 * q^70 - 1584 * q^71 - 7632 * q^72 + 1816 * q^73 - 4880 * q^74 - 1656 * q^75 + 752 * q^76 - 4952 * q^77 + 5424 * q^78 + 2720 * q^79 + 8840 * q^80 + 3440 * q^81 + 6264 * q^82 + 7496 * q^83 - 288 * q^84 + 6136 * q^85 + 2592 * q^86 + 456 * q^87 + 5776 * q^88 + 11848 * q^90 + 2000 * q^91 + 6184 * q^92 + 7416 * q^93 - 4144 * q^94 - 11384 * q^95 + 368 * q^96 - 4616 * q^97 - 7072 * q^98 + 16320 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(85, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
85.4.r.a	$85$	$4$	85.r	85.r	$16$	$200$	$25$	$5.015$		None		✓	✓	✓	85.4.o.a	$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)		$\mathrm{SU}(2)[C_{16}]$