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

• Label: 740.1.v
• Level: $740$
• Weight: $1$
• Character orbit: 740.v
• Rep. character: $\chi_{740}(159,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $114$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	740.v (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 740 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(114\)
Trace bound:			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	12	12	0
Cusp forms	4	4	0
Eisenstein series	8	8	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^4 - 3 * q^5 + 2 * q^9 - 2 * q^10 - 2 * q^16 + 3 * q^20 + q^25 - 8 * q^26 - 2 * q^34 - 4 * q^36 + q^40 + 2 * q^41 + 2 * q^49 + 3 * q^50 + 6 * q^61 + 4 * q^64 - 2 * q^65 + 4 * q^74 - 2 * q^81 - 2 * q^85 - 6 * q^89 - q^90

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.v.a	$740$	$1$	740.v	740.v	$6$	$2$	$1$	$0.369$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-1}) \)	None		✓			740.1.v.a	$4$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)	$1$		\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+q^{8}+\zeta_{6}q^{9}+\cdots\)
740.1.v.b	$740$	$1$	740.v	740.v	$6$	$2$	$1$	$0.369$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-1}) \)	None		✓			740.1.v.a	$4$	$0$	\(1\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}-q^{8}+\zeta_{6}q^{9}+\cdots\)