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

• Label: 85.4.b
• Level: $85$
• Weight: $4$
• Character orbit: 85.b
• Rep. character: $\chi_{85}(69,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	85.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
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	28	24	4
Cusp forms	24	24	0
Eisenstein series	4	0	4

Trace form

24 * q - 96 * q^4 - 8 * q^5 + 16 * q^6 - 180 * q^9 - 42 * q^10 + 60 * q^11 - 76 * q^14 + 124 * q^15 + 240 * q^16 + 100 * q^19 - 82 * q^20 - 128 * q^21 + 204 * q^24 + 124 * q^25 - 100 * q^26 - 464 * q^29 - 108 * q^30 + 36 * q^31 - 136 * q^34 - 104 * q^35 + 604 * q^36 - 264 * q^39 + 518 * q^40 + 816 * q^41 - 104 * q^44 + 56 * q^45 + 208 * q^46 + 24 * q^49 - 1880 * q^50 + 408 * q^51 + 300 * q^54 + 1372 * q^55 + 1072 * q^56 + 268 * q^59 - 520 * q^60 + 1424 * q^61 + 24 * q^64 - 2216 * q^65 - 4136 * q^66 + 1800 * q^69 - 212 * q^70 + 196 * q^71 + 2472 * q^74 - 2440 * q^75 - 3188 * q^76 + 2268 * q^79 + 2582 * q^80 - 1216 * q^81 - 1120 * q^84 - 408 * q^85 - 3864 * q^86 + 3244 * q^89 + 2446 * q^90 - 240 * q^91 - 3964 * q^94 - 368 * q^95 - 3096 * q^96 - 1228 * 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.b.a	$85$	$4$	85.b	5.b	$2$	$24$	$24$	$5.015$		None		✓	✓	✓	85.4.b.a	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$