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

• Label: 77.2.b
• Level: $77$
• Weight: $2$
• Character orbit: 77.b
• Rep. character: $\chi_{77}(76,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(16\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	10	10	0
Cusp forms	6	6	0
Eisenstein series	4	4	0

Trace form

6 * q - 10 * q^4 - 2 * q^9 - 8 * q^11 - 2 * q^14 + 20 * q^15 + 6 * q^16 + 22 * q^22 - 28 * q^23 + 10 * q^25 - 30 * q^36 - 16 * q^37 + 20 * q^42 - 20 * q^44 - 22 * q^49 + 20 * q^53 + 66 * q^56 + 48 * q^58 - 58 * q^64 + 36 * q^67 - 20 * q^70 + 4 * q^71 + 2 * q^77 - 80 * q^78 - 26 * q^81 - 4 * q^86 - 26 * q^88 - 40 * q^91 + 80 * q^92 + 60 * q^93 + 36 * 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.b.a	$77$	$2$	77.b	77.b	$2$	$2$	$2$	$0.615$	\(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{-7}) \)		✓			77.2.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{2}-5q^{4}-\beta q^{7}+3\beta q^{8}+3q^{9}+\cdots\)
77.2.b.b	$77$	$2$	77.b	77.b	$2$	$4$	$4$	$0.615$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		✓	✓		77.2.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+\beta _{3}q^{3}-\beta _{3}q^{5}+(2\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots\)