Space of modular forms of level 209, weight 2, and Character 209.j

• Label: 209.2.j
• Level: $209$
• Weight: $2$
• Character orbit: 209.j
• Rep. character: $\chi_{209}(23,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $96$
• Newform subspaces: $3$
• Sturm bound: $40$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.j (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(40\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(209, [\chi])\).

	Total	New	Old
Modular forms	132	96	36
Cusp forms	108	96	12
Eisenstein series	24	0	24

Trace form

\( 96 q - 12 q^{4} - 12 q^{6} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(209, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
209.2.j.a	$209$	$2$	209.j	19.e	$9$	$6$	$1$	$1.669$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(3\)	\(0\)	\(6\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{2}+\cdots\)
209.2.j.b	$209$	$2$	209.j	19.e	$9$	$42$	$7$	$1.669$		None		$2$	$0$	\(-3\)	\(0\)	\(-6\)	\(-6\)		$\mathrm{SU}(2)[C_{9}]$
209.2.j.c	$209$	$2$	209.j	19.e	$9$	$48$	$8$	$1.669$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(209, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(209, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)