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

• Label: 209.2.n
• Level: $209$
• Weight: $2$
• Character orbit: 209.n
• Rep. character: $\chi_{209}(26,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $144$
• Newform subspaces: $1$
• Sturm bound: $40$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.n (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 209 \)
Character field:			\(\Q(\zeta_{15})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(40\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	176	176	0
Cusp forms	144	144	0
Eisenstein series	32	32	0

Trace form

\( 144 q - 5 q^{2} - q^{3} + 13 q^{4} - 5 q^{5} - 14 q^{6} - 18 q^{7} - 8 q^{8} + 17 q^{9} + O(q^{10}) \)

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.n.a	$209$	$2$	209.n	209.n	$15$	$144$	$18$	$1.669$		None		$4$	$0$	\(-5\)	\(-1\)	\(-5\)	\(-18\)		$\mathrm{SU}(2)[C_{15}]$