Space of modular forms of level 2009, weight 1, and Character 2009.i

• Label: 2009.1.i
• Level: $2009$
• Weight: $1$
• Character orbit: 2009.i
• Rep. character: $\chi_{2009}(901,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $196$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2009 = 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2009.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 287 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(196\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2009, [\chi])\).

	Total	New	Old
Modular forms	28	20	8
Cusp forms	12	12	0
Eisenstein series	16	8	8

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q + 2 q^{2} - 4 q^{4} - 8 q^{8} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2009, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2009.1.i.a	$2009$	$1$	2009.i	287.i	$6$	$6$	$3$	$1.003$	6.0.64827.1	$D_{7}$	\(\Q(\sqrt{-287}) \)	None		$4$	$0$	\(1\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
2009.1.i.b	$2009$	$1$	2009.i	287.i	$6$	$6$	$3$	$1.003$	6.0.64827.1	$D_{7}$	\(\Q(\sqrt{-287}) \)	None		$4$	$0$	\(1\)	\(1\)	\(0\)	\(0\)	$1$		\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots\)