Space of modular forms of level 1740, weight 1, and Character 1740.v

• Label: 1740.1.v
• Level: $1740$
• Weight: $1$
• Character orbit: 1740.v
• Rep. character: $\chi_{1740}(347,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $360$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1740 = 2^{2} \cdot 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1740.v (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1740 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(360\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1740, [\chi])\).

	Total	New	Old
Modular forms	40	40	0
Cusp forms	24	24	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	24	0	0	0

Trace form

\( 24 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1740, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1740.1.v.a	$1740$	$1$	1740.v	1740.v	$4$	$4$	$2$	$0.868$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-29}) \)	None		$8$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q+\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}-q^{5}-\zeta_{8}^{2}q^{6}+\cdots\)
1740.1.v.b	$1740$	$1$	1740.v	1740.v	$4$	$4$	$2$	$0.868$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-29}) \)	None		$8$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$		\(q-\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+q^{5}+\zeta_{8}^{2}q^{6}+\cdots\)
1740.1.v.c	$1740$	$1$	1740.v	1740.v	$4$	$8$	$4$	$0.868$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-29}) \)	None		$8$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q+\zeta_{24}^{9}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{6}q^{4}+\cdots\)
1740.1.v.d	$1740$	$1$	1740.v	1740.v	$4$	$8$	$4$	$0.868$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-29}) \)	None		$8$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$		\(q-\zeta_{24}^{3}q^{2}-\zeta_{24}^{7}q^{3}+\zeta_{24}^{6}q^{4}+\cdots\)