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

• Label: 740.1.cb
• Level: $740$
• Weight: $1$
• Character orbit: 740.cb
• Rep. character: $\chi_{740}(87,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $12$
• 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.cb (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 740 \)
Character field:			\(\Q(\zeta_{36})\)
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	60	60	0
Cusp forms	12	12	0
Eisenstein series	48	48	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

\( 12 q + 6 q^{8} + 6 q^{20} - 6 q^{41} - 12 q^{50} - 12 q^{61} - 6 q^{64} - 6 q^{73} - 6 q^{74}+O(q^{100}) \)

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.cb.a	$740$	$1$	740.cb	740.bb	$36$	$12$	$1$	$0.369$	\(\Q(\zeta_{36})\)	$D_{36}$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	740.1.bw.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{36}^{8}q^{2}+\zeta_{36}^{16}q^{4}+\zeta_{36}^{14}q^{5}+\cdots\)