Space of modular forms of level 740, weight 1, and Character 740.bj

• Label: 740.1.bj
• Level: $740$
• Weight: $1$
• Character orbit: 740.bj
• Rep. character: $\chi_{740}(103,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $114$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	740.bj (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 740 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(114\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(740, [\chi])\).

	Total	New	Old
Modular forms	20	20	0
Cusp forms	4	4	0
Eisenstein series	16	16	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^8 - 2 * q^10 - 2 * q^16 - 4 * q^20 - 2 * q^25 - 2 * q^29 + 2 * q^32 + 2 * q^37 - 2 * q^40 + 6 * q^41 - 4 * q^50 - 2 * q^53 + 2 * q^58 - 4 * q^61 + 4 * q^64 + 4 * q^73 + 4 * q^74 + 2 * q^80 + 2 * q^81 + 2 * q^89

Decomposition of \(S_{1}^{\mathrm{new}}(740, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
740.1.bj.a	$740$	$1$	740.bj	740.aj	$12$	$4$	$1$	$0.369$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	740.1.bj.a	$4$	$0$	\(2\)	\(0\)	\(2\)	\(0\)	$1$		\(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{5}+\cdots\)