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

• Label: 740.1.t
• Level: $740$
• Weight: $1$
• Character orbit: 740.t
• Rep. character: $\chi_{740}(549,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $114$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	740.t (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(114\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	16	4	12
Cusp forms	4	4	0
Eisenstein series	12	0	12

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

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

Trace form

\( 4 q + 2 q^{5} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
740.1.t.a	$740$	$1$	740.t	185.j	$4$	$2$	$1$	$0.369$	\(\Q(\sqrt{-1}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)	$1$		\(q-q^{3}+q^{5}-iq^{7}-iq^{11}-q^{15}+\cdots\)
740.1.t.b	$740$	$1$	740.t	185.j	$4$	$2$	$1$	$0.369$	\(\Q(\sqrt{-1}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q+q^{3}+iq^{5}+iq^{7}-iq^{11}+iq^{15}+\cdots\)