Space of modular forms of level 966, weight 2, and Character 966.h

• Label: 966.2.h
• Level: $966$
• Weight: $2$
• Character orbit: 966.h
• Rep. character: $\chi_{966}(827,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 69 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(966, [\chi])\).

	Total	New	Old
Modular forms	200	48	152
Cusp forms	184	48	136
Eisenstein series	16	0	16

Trace form

48 * q + 8 * q^3 - 48 * q^4 - 8 * q^9 - 8 * q^12 + 16 * q^13 + 48 * q^16 + 8 * q^18 - 24 * q^25 + 32 * q^27 - 32 * q^31 + 8 * q^36 - 16 * q^39 - 8 * q^46 + 8 * q^48 - 48 * q^49 - 16 * q^52 - 24 * q^54 + 32 * q^55 + 8 * q^58 - 48 * q^64 - 48 * q^69 - 8 * q^70 - 8 * q^72 - 64 * q^73 + 96 * q^75 + 24 * q^78 - 16 * q^81 - 16 * q^82 - 32 * q^85 + 40 * q^87 + 32 * q^93 + 16 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(966, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
966.2.h.a	$966$	$2$	966.h	69.c	$2$	$24$	$24$	$7.714$		None		✓			966.2.h.a	$2$	$0$	\(0\)	\(4\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
966.2.h.b	$966$	$2$	966.h	69.c	$2$	$24$	$24$	$7.714$		None		✓			966.2.h.a	$2$	$0$	\(0\)	\(4\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(966, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(966, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)