Space of modular forms of level 952, weight 2, and Character 952.cl

• Label: 952.2.cl
• Level: $952$
• Weight: $2$
• Character orbit: 952.cl
• Rep. character: $\chi_{952}(125,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $1120$
• Newform subspaces: $1$
• Sturm bound: $288$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 952 = 2^{3} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	952.cl (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 952 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(288\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(952, [\chi])\).

	Total	New	Old
Modular forms	1184	1184	0
Cusp forms	1120	1120	0
Eisenstein series	64	64	0

Trace form

1120 * q - 16 * q^2 - 16 * q^4 - 16 * q^7 - 16 * q^8 - 32 * q^9 - 8 * q^14 - 32 * q^15 - 32 * q^18 - 16 * q^22 - 32 * q^23 - 32 * q^25 - 56 * q^28 - 144 * q^30 - 16 * q^32 - 16 * q^36 - 32 * q^39 + 40 * q^42 + 48 * q^44 - 16 * q^46 - 16 * q^49 - 48 * q^56 - 32 * q^57 - 16 * q^58 - 16 * q^60 - 16 * q^63 - 16 * q^64 - 32 * q^65 - 80 * q^70 - 32 * q^71 - 16 * q^72 - 16 * q^74 - 16 * q^78 - 32 * q^79 - 32 * q^81 + 48 * q^86 - 16 * q^88 - 128 * q^92 - 32 * q^95 - 144 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(952, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
952.2.cl.a	$952$	$2$	952.cl	952.bl	$16$	$1120$	$140$	$7.602$		None		✓	✓	✓	952.2.cl.a	$8$	$0$	\(-16\)	\(0\)	\(0\)	\(-16\)		$\mathrm{SU}(2)[C_{16}]$