Space of modular forms of level 77, weight 4, and Character 77.i

• Label: 77.4.i
• Level: $77$
• Weight: $4$
• Character orbit: 77.i
• Rep. character: $\chi_{77}(10,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $44$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(77, [\chi])\).

	Total	New	Old
Modular forms	52	52	0
Cusp forms	44	44	0
Eisenstein series	8	8	0

Trace form

44 * q - 6 * q^3 + 88 * q^4 - 30 * q^5 + 192 * q^9 + 13 * q^11 - 54 * q^12 - 156 * q^14 - 204 * q^15 - 500 * q^16 + 112 * q^22 - 26 * q^23 - 88 * q^25 + 642 * q^26 + 822 * q^31 - 801 * q^33 + 2196 * q^36 + 122 * q^37 + 120 * q^38 - 1940 * q^42 + 256 * q^44 - 2640 * q^45 - 462 * q^47 + 244 * q^49 + 1162 * q^53 + 3706 * q^56 - 918 * q^58 + 462 * q^59 - 3000 * q^60 - 10020 * q^64 - 2400 * q^66 + 950 * q^67 + 3578 * q^70 + 4376 * q^71 + 6552 * q^75 + 877 * q^77 + 4280 * q^78 + 7770 * q^80 + 2350 * q^81 - 5214 * q^82 + 3146 * q^86 + 3764 * q^88 - 3966 * q^89 - 7236 * q^91 + 1116 * q^92 - 2126 * q^93 - 5240 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(77, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
77.4.i.a	$77$	$4$	77.i	77.i	$6$	$44$	$22$	$4.543$		None		✓	✓	✓	77.4.i.a	$4$	$0$	\(0\)	\(-6\)	\(-30\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$