Space of modular forms of level 89, weight 2, and Character 89.g

• Label: 89.2.g
• Level: $89$
• Weight: $2$
• Character orbit: 89.g
• Rep. character: $\chi_{89}(5,\cdot)$
• Character field: $\Q(\zeta_{44})$
• Dimension: $140$
• Newform subspaces: $1$
• Sturm bound: $15$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	89.g (of order \(44\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 89 \)
Character field:			\(\Q(\zeta_{44})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(15\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(89, [\chi])\).

	Total	New	Old
Modular forms	180	180	0
Cusp forms	140	140	0
Eisenstein series	40	40	0

Trace form

140 * q - 20 * q^2 - 20 * q^3 - 32 * q^4 - 22 * q^5 - 14 * q^6 - 20 * q^7 - 16 * q^8 - 22 * q^10 - 18 * q^11 + 6 * q^12 - 18 * q^13 + 76 * q^14 - 36 * q^15 - 40 * q^16 - 22 * q^17 - 22 * q^18 - 12 * q^19 - 22 * q^20 - 22 * q^21 + 66 * q^22 - 8 * q^23 - 8 * q^24 - 16 * q^25 + 6 * q^26 + 40 * q^27 - 4 * q^28 - 38 * q^29 + 104 * q^30 - 26 * q^31 - 8 * q^32 - 16 * q^33 + 20 * q^35 - 22 * q^36 - 22 * q^38 - 54 * q^39 + 88 * q^40 - 34 * q^41 - 22 * q^42 + 126 * q^43 + 2 * q^44 - 18 * q^45 - 32 * q^46 - 22 * q^47 + 220 * q^48 - 22 * q^49 - 36 * q^50 + 20 * q^51 - 18 * q^52 + 66 * q^53 - 74 * q^54 + 100 * q^56 + 14 * q^57 - 46 * q^58 + 48 * q^59 - 74 * q^60 + 62 * q^61 - 8 * q^62 - 66 * q^63 + 184 * q^64 + 20 * q^65 + 112 * q^66 - 46 * q^67 + 22 * q^68 + 242 * q^69 + 16 * q^70 - 22 * q^71 + 154 * q^72 - 24 * q^73 + 32 * q^74 - 98 * q^75 - 90 * q^76 + 90 * q^77 - 218 * q^78 - 66 * q^79 - 110 * q^80 - 26 * q^81 + 90 * q^82 - 106 * q^83 - 330 * q^84 + 12 * q^85 - 114 * q^86 - 42 * q^87 - 296 * q^88 - 102 * q^89 - 12 * q^90 - 58 * q^91 - 146 * q^92 + 52 * q^93 - 110 * q^94 + 114 * q^95 - 374 * q^96 - 40 * q^97 + 88 * q^98 - 132 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(89, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
89.2.g.a	$89$	$2$	89.g	89.g	$44$	$140$	$7$	$0.711$		None		✓	✓	✓	89.2.g.a	$2$	$0$	\(-20\)	\(-20\)	\(-22\)	\(-20\)		$\mathrm{SU}(2)[C_{44}]$