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

• Label: 209.2.k
• Level: $209$
• Weight: $2$
• Character orbit: 209.k
• Rep. character: $\chi_{209}(18,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $40$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.k (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 209 \)
Character field:			\(\Q(\zeta_{10})\)
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	88	88	0
Cusp forms	72	72	0
Eisenstein series	16	16	0

Trace form

\( 72 q - 22 q^{4} - 8 q^{5} - 20 q^{6} - 5 q^{7} + 20 q^{9} + O(q^{10}) \)

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.k.a	$209$	$2$	209.k	209.k	$10$	$8$	$2$	$1.669$	8.0.2036265625.1	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(-15\)	$1$	$\mathrm{U}(1)[D_{10}]$	\(q-2\beta _{6}q^{4}+(\beta _{1}-\beta _{3}+\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
209.2.k.b	$209$	$2$	209.k	209.k	$10$	$8$	$2$	$1.669$	8.0.484000000.9	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-\beta _{1}-\beta _{4})q^{2}+(-1-\beta _{2}-3\beta _{3}+\cdots)q^{4}+\cdots\)
209.2.k.c	$209$	$2$	209.k	209.k	$10$	$56$	$14$	$1.669$		None		$4$	$0$	\(0\)	\(0\)	\(-10\)	\(20\)		$\mathrm{SU}(2)[C_{10}]$