Space of modular forms of level 309, weight 1, and Character 309.l

• Label: 309.1.l
• Level: $309$
• Weight: $1$
• Character orbit: 309.l
• Rep. character: $\chi_{309}(8,\cdot)$
• Character field: $\Q(\zeta_{34})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $34$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 309 = 3 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	309.l (of order \(34\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 309 \)
Character field:			\(\Q(\zeta_{34})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(34\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(309, [\chi])\).

	Total	New	Old
Modular forms	48	48	0
Cusp forms	16	16	0
Eisenstein series	32	32	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q - q^{3} - q^{4} - 2 q^{7} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(309, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
309.1.l.a	$309$	$1$	309.l	309.l	$34$	$16$	$1$	$0.154$	\(\Q(\zeta_{34})\)	$D_{17}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)	$1$		\(q+\zeta_{34}^{6}q^{3}-\zeta_{34}^{7}q^{4}+(\zeta_{34}^{4}-\zeta_{34}^{9}+\cdots)q^{7}+\cdots\)