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

• Label: 77.2.n
• Level: $77$
• Weight: $2$
• Character orbit: 77.n
• Rep. character: $\chi_{77}(17,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.n (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{30})\)
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	80	80	0
Cusp forms	48	48	0
Eisenstein series	32	32	0

Trace form

\( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
77.2.n.a	$77$	$2$	77.n	77.n	$30$	$48$	$6$	$0.615$		None		$4$	$0$	\(-5\)	\(-9\)	\(-15\)	\(-5\)		$\mathrm{SU}(2)[C_{30}]$