Space of modular forms of level 760, weight 1, and Character 760.bz

• Label: 760.1.bz
• Level: $760$
• Weight: $1$
• Character orbit: 760.bz
• Rep. character: $\chi_{760}(99,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $8$

Defining parameters

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	760.bz (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 760 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(760, [\chi])\).

	Total	New	Old
Modular forms	36	36	0
Cusp forms	12	12	0
Eisenstein series	24	24	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(760, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
760.1.bz.a	$760$	$1$	760.bz	760.az	$18$	$6$	$1$	$0.379$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-10}) \)	None		✓			760.1.bz.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}-\zeta_{18}^{5}q^{5}+\cdots\)
760.1.bz.b	$760$	$1$	760.bz	760.az	$18$	$6$	$1$	$0.379$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-10}) \)	None		✓			760.1.bz.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+\zeta_{18}^{5}q^{5}+\cdots\)