Space of modular forms of level 1424, weight 1, and Character 1424.bt

• Label: 1424.1.bt
• Level: $1424$
• Weight: $1$
• Character orbit: 1424.bt
• Rep. character: $\chi_{1424}(47,\cdot)$
• Character field: $\Q(\zeta_{44})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1424 = 2^{4} \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1424.bt (of order \(44\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 356 \)
Character field:			\(\Q(\zeta_{44})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1424, [\chi])\).

	Total	New	Old
Modular forms	140	20	120
Cusp forms	20	20	0
Eisenstein series	120	0	120

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	20	0	0	0

Trace form

\( 20 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1424, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1424.1.bt.a	$1424$	$1$	1424.bt	356.n	$44$	$20$	$1$	$0.711$	\(\Q(\zeta_{44})\)	$D_{44}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{44}^{2}+\zeta_{44}^{8})q^{5}+\zeta_{44}^{19}q^{9}+(\zeta_{44}^{7}+\cdots)q^{13}+\cdots\)