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

• Label: 209.2.u
• Level: $209$
• Weight: $2$
• Character orbit: 209.u
• Rep. character: $\chi_{209}(4,\cdot)$
• Character field: $\Q(\zeta_{45})$
• Dimension: $432$
• Newform subspaces: $1$
• Sturm bound: $40$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.u (of order \(45\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 209 \)
Character field:			\(\Q(\zeta_{45})\)
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	528	528	0
Cusp forms	432	432	0
Eisenstein series	96	96	0

Trace form

\( 432 q - 18 q^{2} - 24 q^{3} - 18 q^{4} - 18 q^{5} - 9 q^{6} - 27 q^{8} - 36 q^{9} + O(q^{10}) \)

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.u.a	$209$	$2$	209.u	209.u	$45$	$432$	$18$	$1.669$		None		$4$	$0$	\(-18\)	\(-24\)	\(-18\)	\(0\)		$\mathrm{SU}(2)[C_{45}]$