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

• Label: 77.2.l
• Level: $77$
• Weight: $2$
• Character orbit: 77.l
• Rep. character: $\chi_{77}(6,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.l (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{10})\)
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	40	40	0
Cusp forms	24	24	0
Eisenstein series	16	16	0

Trace form

\( 24 q - 10 q^{2} - 10 q^{7} + 2 q^{9} + O(q^{10}) \)

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.l.a	$77$	$2$	77.l	77.l	$10$	$8$	$2$	$0.615$	8.0.37515625.1	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{10}]$	\(q+(1-\beta _{1}+\beta _{3}+\beta _{4}+\beta _{5}-\beta _{6})q^{2}+\cdots\)
77.2.l.b	$77$	$2$	77.l	77.l	$10$	$16$	$4$	$0.615$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(-10\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-1-\beta _{9}-\beta _{11})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)