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

• Label: 1700.1.h
• Level: $1700$
• Weight: $1$
• Character orbit: 1700.h
• Rep. character: $\chi_{1700}(951,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $7$
• Sturm bound: $270$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1700 = 2^{2} \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1700.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 68 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(270\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	24	15	9
Cusp forms	12	9	3
Eisenstein series	12	6	6

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	9	0	0	0

Trace form

\( 9 q + q^{2} + 9 q^{4} + q^{8} + 7 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1700.1.h.a	$1700$	$1$	1700.h	68.d	$2$	$1$	$1$	$0.848$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-17}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
1700.1.h.b	$1700$	$1$	1700.h	68.d	$2$	$1$	$1$	$0.848$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-17}) \)	None	✓	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(1\)	$1$		\(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
1700.1.h.c	$1700$	$1$	1700.h	68.d	$2$	$1$	$1$	$0.848$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-17}) \)	None	✓	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
1700.1.h.d	$1700$	$1$	1700.h	68.d	$2$	$1$	$1$	$0.848$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \)	\(\Q(\sqrt{17}) \)	✓	$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{4}+q^{8}-q^{9}+2q^{13}+q^{16}+\cdots\)
1700.1.h.e	$1700$	$1$	1700.h	68.d	$2$	$1$	$1$	$0.848$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-17}) \)	None	✓	$2$	$0$	\(1\)	\(1\)	\(0\)	\(1\)	$1$		\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
1700.1.h.f	$1700$	$1$	1700.h	68.d	$2$	$2$	$2$	$0.848$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-17}) \)	None	✓	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+\beta q^{7}-q^{8}+\cdots\)
1700.1.h.g	$1700$	$1$	1700.h	68.d	$2$	$2$	$2$	$0.848$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-17}) \)	None	✓	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}+\beta q^{7}+q^{8}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1700, [\chi]) \cong \)