Space of modular forms of level 968, weight 2, and Character 968.ba

• Label: 968.2.ba
• Level: $968$
• Weight: $2$
• Character orbit: 968.ba
• Rep. character: $\chi_{968}(19,\cdot)$
• Character field: $\Q(\zeta_{110})$
• Dimension: $5200$
• Newform subspaces: $2$
• Sturm bound: $264$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.ba (of order \(110\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 968 \)
Character field:			\(\Q(\zeta_{110})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(264\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(968, [\chi])\).

	Total	New	Old
Modular forms	5360	5360	0
Cusp forms	5200	5200	0
Eisenstein series	160	160	0

Trace form

5200 * q - 39 * q^2 - 60 * q^3 - 43 * q^4 - 17 * q^6 - 39 * q^8 - 1320 * q^9 - 44 * q^10 - 76 * q^11 - q^12 - 48 * q^14 - 39 * q^16 - 78 * q^17 - 9 * q^18 - 78 * q^19 - 18 * q^20 - 57 * q^22 + 112 * q^24 - 204 * q^25 - 44 * q^26 + 60 * q^27 - 14 * q^28 - 41 * q^30 - 44 * q^32 - 16 * q^33 - 30 * q^34 - 78 * q^35 + 3 * q^36 - 38 * q^38 - 85 * q^40 - 78 * q^41 - 65 * q^42 - 88 * q^43 - 65 * q^44 - 84 * q^46 - 31 * q^48 + 36 * q^49 - 27 * q^50 - 12 * q^51 - 238 * q^52 - 77 * q^54 - 141 * q^56 - 56 * q^57 - 55 * q^58 - 82 * q^59 - 33 * q^60 + 91 * q^62 - 103 * q^64 - 88 * q^65 + 27 * q^66 - 32 * q^67 - 104 * q^68 + 8 * q^70 + 32 * q^72 - 78 * q^73 + 56 * q^74 - 56 * q^75 - 99 * q^76 - 129 * q^78 - 143 * q^80 - 1088 * q^81 - 19 * q^82 - 178 * q^83 + 39 * q^84 + 17 * q^86 + 17 * q^88 - 72 * q^89 + 118 * q^90 - 182 * q^91 - 50 * q^92 - 25 * q^94 + 99 * q^96 - 66 * q^97 + 44 * q^98 + 48 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(968, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
968.2.ba.a	$968$	$2$	968.ba	968.aa	$110$	$80$	$2$	$7.730$		\(\Q(\sqrt{-2}) \)		✓			968.2.ba.a	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{110}]$
968.2.ba.b	$968$	$2$	968.ba	968.aa	$110$	$5120$	$128$	$7.730$		None		✓	✓		968.2.ba.b	$4$	$0$	\(-39\)	\(-64\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{110}]$