Space of modular forms of level 1320, weight 2, and Character 1320.bu

• Label: 1320.2.bu
• Level: $1320$
• Weight: $2$
• Character orbit: 1320.bu
• Rep. character: $\chi_{1320}(1033,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $72$
• Newform subspaces: $2$
• Sturm bound: $576$
• Trace bound: $7$

Defining parameters

Level:	$N$	$=$	$1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1320.bu (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$55$
Character field:			$\Q(i)$
Newform subspaces:			$2$
Sturm bound:			$576$
Trace bound:			$7$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(1320, [\chi])$.

	Total	New	Old
Modular forms	608	72	536
Cusp forms	544	72	472
Eisenstein series	64	0	64

Trace form

$72 q - 8 q^{11} - 8 q^{15} + 48 q^{23} - 16 q^{25} - 16 q^{31} - 12 q^{33} + 16 q^{37} - 32 q^{47} + 4 q^{55} + 32 q^{67} + 16 q^{75} - 48 q^{77} - 72 q^{81} + 32 q^{91} + 48 q^{93} + 24 q^{97}+O(q^{100})$

Decomposition of $S_{2}^{\mathrm{new}}(1320, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1320.2.bu.a	$1320$	$2$	1320.bu	55.e	$4$	$36$	$18$	$10.540$		None		✓			1320.2.bu.a	$2$	$0$	$0$	$0$	$0$	$-4$		$\mathrm{SU}(2)[C_{4}]$
1320.2.bu.b	$1320$	$2$	1320.bu	55.e	$4$	$36$	$18$	$10.540$		None		✓			1320.2.bu.a	$2$	$0$	$0$	$0$	$0$	$4$		$\mathrm{SU}(2)[C_{4}]$

Decomposition of $S_{2}^{\mathrm{old}}(1320, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(1320, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(55, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(110, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(165, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(220, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(330, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(440, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(660, [\chi])$$^{\oplus 2}$