Space of modular forms of level 207, weight 2, and Character 207.o

• Label: 207.2.o
• Level: $207$
• Weight: $2$
• Character orbit: 207.o
• Rep. character: $\chi_{207}(5,\cdot)$
• Character field: $\Q(\zeta_{66})$
• Dimension: $440$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 207 \)
Character field:			\(\Q(\zeta_{66})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(207, [\chi])\).

	Total	New	Old
Modular forms	520	520	0
Cusp forms	440	440	0
Eisenstein series	80	80	0

Trace form

\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(207, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
207.2.o.a	$207$	$2$	207.o	207.o	$66$	$440$	$22$	$1.653$		None		$4$	$0$	\(-27\)	\(-16\)	\(-33\)	\(-11\)		$\mathrm{SU}(2)[C_{66}]$