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

• Label: 77.4.b
• Level: $77$
• Weight: $4$
• Character orbit: 77.b
• Rep. character: $\chi_{77}(76,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $2$
• Sturm bound: $32$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	77.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(32\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	26	26	0
Cusp forms	22	22	0
Eisenstein series	4	4	0

Trace form

\( 22 q - 94 q^{4} - 198 q^{9} + O(q^{10}) \)

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.b.a	$77$	$4$	77.b	77.b	$2$	$2$	$2$	$4.543$	\(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{-7}) \)		✓			77.4.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{2}+q^{4}-7\beta q^{7}-9\beta q^{8}+3^{3}q^{9}+\cdots\)
77.4.b.b	$77$	$4$	77.b	77.b	$2$	$20$	$20$	$4.543$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓		77.4.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{10}q^{2}+\beta _{11}q^{3}+(-5+\beta _{3})q^{4}+\cdots\)