Space of modular forms of level 77, weight 2, and Character 77.i

• Label: 77.2.i
• Level: $77$
• Weight: $2$
• Character orbit: 77.i
• Rep. character: $\chi_{77}(10,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(77, [\chi])\).

	Total	New	Old
Modular forms	20	20	0
Cusp forms	12	12	0
Eisenstein series	8	8	0

Trace form

12 * q - 6 * q^3 + 4 * q^4 - 4 * q^9 - 4 * q^11 - 18 * q^12 + 8 * q^14 - 20 * q^15 + 12 * q^16 - 4 * q^22 - 20 * q^23 + 14 * q^25 + 18 * q^26 + 6 * q^31 + 18 * q^33 - 12 * q^36 + 16 * q^37 - 48 * q^38 + 16 * q^42 + 20 * q^44 + 54 * q^45 - 18 * q^47 + 16 * q^49 - 2 * q^53 + 18 * q^56 - 6 * q^58 - 12 * q^59 + 28 * q^64 - 42 * q^66 - 24 * q^67 - 58 * q^70 + 20 * q^71 - 78 * q^75 - 50 * q^77 + 8 * q^78 + 30 * q^80 + 14 * q^81 + 54 * q^82 - 38 * q^86 - 4 * q^88 - 66 * q^89 + 22 * q^91 - 20 * q^92 + 12 * q^93 + 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(77, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
77.2.i.a	$77$	$2$	77.i	77.i	$6$	$12$	$6$	$0.615$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓	✓	77.2.i.a	$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}+\beta _{7})q^{2}+(-1+\beta _{2}-\beta _{8}-\beta _{9}+\cdots)q^{3}+\cdots\)