Space of modular forms of level 700, weight 1, and Character 700.j

• Label: 700.1.j
• Level: $700$
• Weight: $1$
• Character orbit: 700.j
• Rep. character: $\chi_{700}(307,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	700.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 140 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(700, [\chi])\).

	Total	New	Old
Modular forms	36	20	16
Cusp forms	12	12	0
Eisenstein series	24	8	16

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q - 12 q^{46} - 12 q^{56} - 12 q^{81} + 12 q^{86}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(700, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
700.1.j.a	$700$	$1$	700.j	140.j	$4$	$4$	$2$	$0.349$	\(\Q(\zeta_{8})\)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{35}) \)		✓			700.1.j.a	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{8}+\cdots\)
700.1.j.b	$700$	$1$	700.j	140.j	$4$	$8$	$4$	$0.349$	\(\Q(\zeta_{24})\)	$D_{6}$	\(\Q(\sqrt{-7}) \)	None		✓	✓		700.1.j.b	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{3}q^{7}+\cdots\)