Space of modular forms of level 207, weight 4, and Character 207.c

• Label: 207.4.c
• Level: $207$
• Weight: $4$
• Character orbit: 207.c
• Rep. character: $\chi_{207}(206,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(207, [\chi])\).

	Total	New	Old
Modular forms	76	24	52
Cusp forms	68	24	44
Eisenstein series	8	0	8

Trace form

24 * q - 120 * q^4 + 96 * q^13 + 960 * q^16 + 648 * q^25 - 96 * q^31 + 1176 * q^46 - 1992 * q^49 - 2280 * q^52 - 528 * q^55 + 3048 * q^58 - 5688 * q^64 + 7896 * q^70 - 1152 * q^73 + 3096 * q^82 + 4080 * q^85 - 12504 * q^94

Decomposition of \(S_{4}^{\mathrm{new}}(207, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
207.4.c.a	$207$	$4$	207.c	69.c	$2$	$24$	$24$	$12.213$		None		✓	✓	✓	207.4.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(207, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(207, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)