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

• Label: 1700.1.br
• Level: $1700$
• Weight: $1$
• Character orbit: 1700.br
• Rep. character: $\chi_{1700}(107,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $8$
• 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.br (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 340 \)
Character field:			\(\Q(\zeta_{16})\)
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	120	40	80
Cusp forms	24	8	16
Eisenstein series	96	32	64

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q - 8 q^{41} - 8 q^{72} + 8 q^{73} + 8 q^{74} - 8 q^{98}+O(q^{100}) \)

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.br.a	$1700$	$1$	1700.br	340.aj	$16$	$8$	$1$	$0.848$	\(\Q(\zeta_{16})\)	$D_{16}$	\(\Q(\sqrt{-1}) \)	None			✓	✓	340.1.bc.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}-\zeta_{16}^{7}q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1700, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1700, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(340, [\chi])\)\(^{\oplus 2}\)