Space of modular forms of level 1400, weight 1, and Character 1400.c

• Label: 1400.1.c
• Level: $1400$
• Weight: $1$
• Character orbit: 1400.c
• Rep. character: $\chi_{1400}(349,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $240$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1400.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 280 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(240\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1400, [\chi])\).

	Total	New	Old
Modular forms	26	10	16
Cusp forms	14	6	8
Eisenstein series	12	4	8

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q + 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1400, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1400.1.c.a	$1400$	$1$	1400.c	280.c	$2$	$2$	$2$	$0.699$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{2}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{2}-q^{4}-iq^{7}+iq^{8}+q^{9}-q^{14}+\cdots\)
1400.1.c.b	$1400$	$1$	1400.c	280.c	$2$	$4$	$4$	$0.699$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{7}-\zeta_{12}^{3}q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1400, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1400, [\chi]) \cong \)