Space of modular forms of level 85, weight 2, and Character 85.o

• Label: 85.2.o
• Level: $85$
• Weight: $2$
• Character orbit: 85.o
• Rep. character: $\chi_{85}(3,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $56$
• Newform subspaces: $1$
• Sturm bound: $18$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.o (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(18\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(85, [\chi])\).

	Total	New	Old
Modular forms	88	88	0
Cusp forms	56	56	0
Eisenstein series	32	32	0

Trace form

56 * q - 8 * q^2 - 8 * q^3 - 8 * q^5 - 16 * q^6 - 8 * q^7 + 8 * q^8 - 24 * q^10 - 16 * q^11 - 32 * q^12 + 32 * q^14 + 16 * q^15 - 8 * q^17 - 16 * q^18 - 32 * q^19 + 32 * q^20 - 16 * q^21 - 8 * q^22 - 8 * q^23 + 16 * q^26 + 40 * q^27 - 8 * q^28 - 72 * q^30 + 16 * q^31 - 24 * q^32 + 16 * q^33 + 32 * q^34 - 16 * q^35 + 48 * q^36 - 40 * q^37 - 16 * q^38 + 16 * q^39 + 48 * q^40 + 24 * q^41 + 56 * q^42 - 8 * q^43 - 8 * q^45 + 64 * q^47 - 56 * q^48 - 32 * q^50 - 16 * q^51 + 48 * q^52 + 40 * q^53 + 64 * q^54 - 40 * q^55 - 16 * q^56 + 48 * q^58 - 80 * q^59 + 72 * q^60 - 16 * q^61 + 40 * q^62 + 64 * q^63 - 32 * q^64 + 32 * q^65 - 16 * q^66 + 64 * q^67 + 40 * q^68 - 104 * q^70 - 32 * q^71 + 24 * q^73 + 40 * q^74 - 96 * q^75 - 80 * q^76 - 120 * q^77 + 80 * q^78 + 40 * q^80 - 64 * q^81 - 80 * q^82 - 96 * q^84 + 16 * q^85 - 64 * q^86 - 16 * q^87 - 160 * q^88 + 48 * q^90 - 64 * q^91 - 40 * q^92 - 16 * q^94 - 24 * q^95 + 16 * q^96 - 88 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(85, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
85.2.o.a	$85$	$2$	85.o	85.o	$16$	$56$	$7$	$0.679$		None		✓	✓	✓	85.2.o.a	$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)		$\mathrm{SU}(2)[C_{16}]$