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

• Label: 1400.1.ba
• Level: $1400$
• Weight: $1$
• Character orbit: 1400.ba
• Rep. character: $\chi_{1400}(51,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $240$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1400.ba (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(240\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	28	16	12
Cusp forms	4	4	0
Eisenstein series	24	12	12

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

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

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.ba.a	$1400$	$1$	1400.ba	56.k	$6$	$4$	$2$	$0.699$	\(\Q(\zeta_{12})\)	$D_{3}$	\(\Q(\sqrt{-10}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{7}+\cdots\)