Space of modular forms of level 207, weight 6, and Character 207.c

• Label: 207.6.c
• Level: $207$
• Weight: $6$
• Character orbit: 207.c
• Rep. character: $\chi_{207}(206,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	207.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 69 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(207, [\chi])\).

	Total	New	Old
Modular forms	124	40	84
Cusp forms	116	40	76
Eisenstein series	8	0	8

Trace form

\( 40 q - 600 q^{4} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(207, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
207.6.c.a	$207$	$6$	207.c	69.c	$2$	$40$	$40$	$33.199$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{6}^{\mathrm{old}}(207, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(207, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)