Space of modular forms of level 69, weight 2, and Character 69.g

• Label: 69.2.g
• Level: $69$
• Weight: $2$
• Character orbit: 69.g
• Rep. character: $\chi_{69}(5,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $60$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.g (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 69 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(69, [\chi])\).

	Total	New	Old
Modular forms	100	100	0
Cusp forms	60	60	0
Eisenstein series	40	40	0

Trace form

60 * q - 11 * q^3 - 10 * q^4 - 14 * q^6 - 22 * q^7 - 11 * q^9 - 22 * q^10 + 4 * q^12 - 22 * q^13 - 46 * q^16 + 12 * q^18 - 22 * q^19 + 22 * q^21 + 50 * q^24 + 8 * q^25 + 10 * q^27 - 22 * q^28 + 33 * q^30 - 22 * q^31 + 22 * q^36 + 22 * q^37 + 13 * q^39 + 132 * q^40 - 11 * q^42 + 22 * q^43 + 66 * q^46 - 58 * q^48 + 68 * q^49 - 11 * q^51 + 94 * q^52 - 33 * q^54 - 44 * q^57 - 8 * q^58 - 121 * q^60 - 66 * q^61 - 66 * q^63 - 20 * q^64 - 66 * q^66 - 44 * q^67 - 66 * q^69 - 132 * q^70 - 101 * q^72 - 44 * q^73 - 44 * q^75 - 110 * q^76 + 84 * q^78 - 66 * q^79 + 77 * q^81 - 132 * q^82 + 77 * q^84 - 44 * q^85 + 73 * q^87 + 66 * q^88 + 176 * q^90 + 116 * q^93 + 100 * q^94 + 85 * q^96 + 44 * q^97 + 121 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(69, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
69.2.g.a	$69$	$2$	69.g	69.g	$22$	$60$	$6$	$0.551$		None		✓	✓	✓	69.2.g.a	$4$	$0$	\(0\)	\(-11\)	\(0\)	\(-22\)		$\mathrm{SU}(2)[C_{22}]$