Space of modular forms of level 1700, weight 1, and Character 1700.cf

• Label: 1700.1.cf
• Level: $1700$
• Weight: $1$
• Character orbit: 1700.cf
• Rep. character: $\chi_{1700}(19,\cdot)$
• Character field: $\Q(\zeta_{40})$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $270$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 1700 = 2^{2} \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1700.cf (of order \(40\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1700 \)
Character field:			\(\Q(\zeta_{40})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(270\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1700, [\chi])\).

	Total	New	Old
Modular forms	96	96	0
Cusp forms	32	32	0
Eisenstein series	64	64	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	32	0	0	0

Trace form

\( 32 q - 4 q^{10} + 8 q^{16} + 16 q^{20} + 4 q^{25} + 8 q^{26} + 8 q^{29} - 8 q^{41} + 4 q^{45} - 20 q^{53} - 16 q^{65} - 8 q^{74} + 4 q^{85} - 4 q^{90}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1700, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1700.1.cf.a	$1700$	$1$	1700.cf	1700.bf	$40$	$16$	$1$	$0.848$	\(\Q(\zeta_{40})\)	$D_{40}$	\(\Q(\sqrt{-1}) \)	None		✓			1700.1.cf.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{40}^{17}q^{2}-\zeta_{40}^{14}q^{4}-\zeta_{40}^{11}q^{5}+\cdots\)
1700.1.cf.b	$1700$	$1$	1700.cf	1700.bf	$40$	$16$	$1$	$0.848$	\(\Q(\zeta_{40})\)	$D_{40}$	\(\Q(\sqrt{-1}) \)	None		✓			1700.1.cf.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{40}^{17}q^{2}-\zeta_{40}^{14}q^{4}+\zeta_{40}^{6}q^{5}+\cdots\)