Space of modular forms of level 1359, weight 1, and Character 1359.bp

• Label: 1359.1.bp
• Level: $1359$
• Weight: $1$
• Character orbit: 1359.bp
• Rep. character: $\chi_{1359}(28,\cdot)$
• Character field: $\Q(\zeta_{50})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $152$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1359 = 3^{2} \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1359.bp (of order \(50\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 151 \)
Character field:			\(\Q(\zeta_{50})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(152\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1359, [\chi])\).

	Total	New	Old
Modular forms	100	40	60
Cusp forms	20	20	0
Eisenstein series	80	20	60

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

\( 20 q + 5 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1359, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1359.1.bp.a	$1359$	$1$	1359.bp	151.j	$50$	$20$	$1$	$0.678$	\(\Q(\zeta_{50})\)	$D_{50}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{50}^{20}q^{4}+(\zeta_{50}^{8}-\zeta_{50}^{14})q^{7}+\cdots\)