Space of modular forms of level 985, weight 2, and Character 985.b

• Label: 985.2.b
• Level: $985$
• Weight: $2$
• Character orbit: 985.b
• Rep. character: $\chi_{985}(789,\cdot)$
• Character field: $\Q$
• Dimension: $98$
• Newform subspaces: $1$
• Sturm bound: $198$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 985 = 5 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	985.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(198\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(985, [\chi])\).

	Total	New	Old
Modular forms	102	98	4
Cusp forms	98	98	0
Eisenstein series	4	0	4

Trace form

98 * q - 98 * q^4 - 2 * q^5 + 4 * q^6 - 102 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^14 - 2 * q^15 + 98 * q^16 - 8 * q^19 - 2 * q^20 + 20 * q^21 + 10 * q^25 - 4 * q^26 - 12 * q^29 - 10 * q^30 - 4 * q^31 + 24 * q^34 + 4 * q^35 + 86 * q^36 + 12 * q^40 - 4 * q^41 + 16 * q^44 - 16 * q^45 - 44 * q^46 - 130 * q^49 + 28 * q^50 + 32 * q^51 - 84 * q^54 + 14 * q^55 - 44 * q^56 - 16 * q^59 + 38 * q^60 + 32 * q^61 - 110 * q^64 + 30 * q^65 + 84 * q^66 + 12 * q^69 + 38 * q^70 + 48 * q^74 + 38 * q^75 - 8 * q^76 - 20 * q^79 - 4 * q^80 + 82 * q^81 - 84 * q^84 - 40 * q^85 - 56 * q^86 - 8 * q^89 + 30 * q^90 + 16 * q^94 + 18 * q^95 - 68 * q^96 - 44 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(985, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
985.2.b.a	$985$	$2$	985.b	5.b	$2$	$98$	$98$	$7.865$		None		✓	✓	✓	985.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$