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

• Label: 1700.1.ct
• Level: $1700$
• Weight: $1$
• Character orbit: 1700.ct
• Rep. character: $\chi_{1700}(3,\cdot)$
• Character field: $\Q(\zeta_{80})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $270$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1700 = 2^{2} \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1700.ct (of order \(80\) and degree \(32\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1700 \)
Character field:			\(\Q(\zeta_{80})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(270\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	160	160	0
Cusp forms	32	32	0
Eisenstein series	128	128	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

\( 32 q - 32 q^{20} + 8 q^{41} + 8 q^{53} - 8 q^{68} + 8 q^{74} - 8 q^{82} - 8 q^{90}+O(q^{100}) \)

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.ct.a	$1700$	$1$	1700.ct	1700.bt	$80$	$32$	$1$	$0.848$	\(\Q(\zeta_{80})\)	$D_{80}$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	1700.1.cm.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{80}^{37}q^{2}-\zeta_{80}^{34}q^{4}-\zeta_{80}^{6}q^{5}+\cdots\)