Space of modular forms of level 712, weight 1, and Character 712.y

• Label: 712.1.y
• Level: $712$
• Weight: $1$
• Character orbit: 712.y
• Rep. character: $\chi_{712}(99,\cdot)$
• Character field: $\Q(\zeta_{44})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $90$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 712 = 2^{3} \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	712.y (of order \(44\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 712 \)
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 \(M_{1}(712, [\chi])\).

	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

\( 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{8} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(712, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
712.1.y.a	$712$	$1$	712.y	712.y	$44$	$20$	$1$	$0.355$	\(\Q(\zeta_{44})\)	$D_{44}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(2\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-\zeta_{44}^{20}q^{2}+(-\zeta_{44}^{3}+\zeta_{44}^{16})q^{3}+\cdots\)