Space of modular forms of level 206, weight 2, and Character 206.e

• Label: 206.2.e
• Level: $206$
• Weight: $2$
• Character orbit: 206.e
• Rep. character: $\chi_{206}(9,\cdot)$
• Character field: $\Q(\zeta_{17})$
• Dimension: $160$
• Newform subspaces: $3$
• Sturm bound: $52$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 206 = 2 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	206.e (of order \(17\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 103 \)
Character field:			\(\Q(\zeta_{17})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(52\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(206, [\chi])\).

	Total	New	Old
Modular forms	448	160	288
Cusp forms	384	160	224
Eisenstein series	64	0	64

Trace form

\( 160 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{7} - 30 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(206, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
206.2.e.a	$206$	$2$	206.e	103.e	$17$	$16$	$1$	$1.645$	\(\Q(\zeta_{34})\)	None		$2$	$0$	\(1\)	\(-3\)	\(15\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{17}]$	\(q-\zeta_{34}^{10}q^{2}+(-\zeta_{34}^{5}+\zeta_{34}^{12}-\zeta_{34}^{15})q^{3}+\cdots\)
206.2.e.b	$206$	$2$	206.e	103.e	$17$	$64$	$4$	$1.645$		None		$2$	$0$	\(4\)	\(3\)	\(-15\)	\(5\)		$\mathrm{SU}(2)[C_{17}]$
206.2.e.c	$206$	$2$	206.e	103.e	$17$	$80$	$5$	$1.645$		None		$2$	$0$	\(-5\)	\(-6\)	\(-6\)	\(-10\)		$\mathrm{SU}(2)[C_{17}]$

Decomposition of \(S_{2}^{\mathrm{old}}(206, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(206, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(103, [\chi])\)\(^{\oplus 2}\)