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

• Label: 209.2.d
• Level: $209$
• Weight: $2$
• Character orbit: 209.d
• Rep. character: $\chi_{209}(208,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $3$
• Sturm bound: $40$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 209 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(40\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	22	22	0
Cusp forms	18	18	0
Eisenstein series	4	4	0

Trace form

18 * q + 12 * q^4 - 2 * q^5 - 30 * q^9 + 5 * q^11 - 40 * q^20 - 16 * q^23 + 28 * q^25 + 20 * q^26 - 88 * q^36 - 32 * q^38 + 128 * q^42 + 62 * q^44 + 34 * q^45 - 6 * q^47 - 44 * q^49 - 27 * q^55 + 20 * q^58 - 4 * q^66 + 17 * q^77 - 124 * q^80 - 46 * q^81 - 28 * q^82 + 88 * q^93 - 25 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
209.2.d.a	$209$	$2$	209.d	209.d	$2$	$2$	$2$	$1.669$	\(\Q(\sqrt{-19}) \)	\(\Q(\sqrt{-19}) \)		✓			209.2.d.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{4}+q^{5}+(1-2\beta )q^{7}+3q^{9}+(3+\cdots)q^{11}+\cdots\)
209.2.d.b	$209$	$2$	209.d	209.d	$2$	$8$	$8$	$1.669$	8.0.3288334336.3	None		✓			209.2.d.b	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}+\beta _{2}q^{3}-\beta _{3}q^{4}+(-1-\beta _{3}+\cdots)q^{5}+\cdots\)
209.2.d.c	$209$	$2$	209.d	209.d	$2$	$8$	$8$	$1.669$	8.0.484000000.9	None		✓			209.2.d.c	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+\beta _{2}q^{3}+(1+2\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots\)