Space of modular forms of level 756, weight 2, and Character 756.cc

• Label: 756.2.cc
• Level: $756$
• Weight: $2$
• Character orbit: 756.cc
• Rep. character: $\chi_{756}(139,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $840$
• Newform subspaces: $1$
• Sturm bound: $288$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.cc (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 756 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(288\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(756, [\chi])\).

	Total	New	Old
Modular forms	888	888	0
Cusp forms	840	840	0
Eisenstein series	48	48	0

Trace form

840 * q - 12 * q^2 - 12 * q^4 - 6 * q^8 - 24 * q^9 - 21 * q^14 - 12 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 - 24 * q^25 - 12 * q^28 + 6 * q^30 + 18 * q^32 - 72 * q^36 - 12 * q^37 - 36 * q^42 - 6 * q^44 - 6 * q^46 - 12 * q^49 - 42 * q^50 - 48 * q^53 - 111 * q^56 + 12 * q^57 - 12 * q^58 - 42 * q^60 - 6 * q^64 + 9 * q^70 + 78 * q^72 - 42 * q^74 - 36 * q^77 - 48 * q^78 - 48 * q^81 - 114 * q^84 - 84 * q^85 + 126 * q^86 - 60 * q^88 - 132 * q^92 - 24 * q^93 + 54 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(756, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
756.2.cc.a	$756$	$2$	756.cc	756.bc	$18$	$840$	$140$	$6.037$		None		✓	✓	✓	756.2.cc.a	$8$	$0$	\(-12\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$