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

• Label: 207.4.k
• Level: $207$
• Weight: $4$
• Character orbit: 207.k
• Rep. character: $\chi_{207}(17,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $240$
• 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.k (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 69 \)
Character field:			\(\Q(\zeta_{22})\)
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	760	240	520
Cusp forms	680	240	440
Eisenstein series	80	0	80

Trace form

240 * q + 120 * q^4 - 96 * q^13 - 960 * q^16 - 648 * q^25 + 96 * q^31 - 3828 * q^34 - 2376 * q^37 + 660 * q^40 + 3432 * q^43 + 6744 * q^46 + 1992 * q^49 + 2940 * q^52 + 1584 * q^55 - 4236 * q^58 - 1056 * q^61 - 2760 * q^64 - 2904 * q^67 - 19512 * q^70 - 960 * q^73 - 2112 * q^76 + 3696 * q^79 + 6936 * q^82 + 4896 * 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.k.a	$207$	$4$	207.k	69.g	$22$	$240$	$24$	$12.213$		None		✓	✓	✓	207.4.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$

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

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