Space of modular forms of level 979, weight 1, and Character 979.v

• Label: 979.1.v
• Level: $979$
• Weight: $1$
• Character orbit: 979.v
• Rep. character: $\chi_{979}(10,\cdot)$
• Character field: $\Q(\zeta_{44})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $90$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 979 = 11 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	979.v (of order \(44\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 979 \)
Character field:			\(\Q(\zeta_{44})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(90\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(979, [\chi])\).

	Total	New	Old
Modular forms	60	60	0
Cusp forms	20	20	0
Eisenstein series	40	40	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	20	0	0	0

Trace form

\( 20 q + 2 q^{3} - 2 q^{4} - 22 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(979, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
979.1.v.a	$979$	$1$	979.v	979.v	$44$	$20$	$1$	$0.489$	\(\Q(\zeta_{44})\)	$D_{44}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{44}^{11}-\zeta_{44}^{20})q^{3}+\zeta_{44}^{12}q^{4}+\cdots\)