Space of modular forms of level 532, weight 2, and Character 532.u

• Label: 532.2.u
• Level: $532$
• Weight: $2$
• Character orbit: 532.u
• Rep. character: $\chi_{532}(83,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $152$
• Newform subspaces: $2$
• Sturm bound: $160$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$532 = 2^{2} \cdot 7 \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	532.u (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$532$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$2$
Sturm bound:			$160$
Trace bound:			$1$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(532, [\chi])$.

	Total	New	Old
Modular forms	168	168	0
Cusp forms	152	152	0
Eisenstein series	16	16	0

Trace form

152 * q - 2 * q^2 - 2 * q^4 - 20 * q^8 - 72 * q^9 - 2 * q^14 - 2 * q^16 + 12 * q^18 - 4 * q^21 + 2 * q^22 + 56 * q^25 + 10 * q^28 - 4 * q^29 - 24 * q^30 - 12 * q^32 + 28 * q^36 - 32 * q^37 + 4 * q^42 + 28 * q^44 - 56 * q^46 + 24 * q^49 + 4 * q^50 - 12 * q^53 + 48 * q^56 - 12 * q^57 + 76 * q^58 + 10 * q^60 - 68 * q^64 - 72 * q^65 - 64 * q^70 + 54 * q^72 + 8 * q^74 + 80 * q^77 + 32 * q^78 - 76 * q^81 - 52 * q^84 - 12 * q^85 - 32 * q^86 + 32 * q^88 + 8 * q^92 - 40 * q^93 - 66 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(532, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
532.2.u.a	$532$	$2$	532.u	532.u	$6$	$16$	$8$	$4.248$	16.0.$\cdots$.16	None		✓			532.2.u.a	$8$	$0$	$-4$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{5}+\beta _{7})q^{2}+(\beta _{1}-\beta _{13})q^{3}+(-\beta _{5}+\cdots)q^{4}+\cdots$
532.2.u.b	$532$	$2$	532.u	532.u	$6$	$136$	$68$	$4.248$		None		✓	✓		532.2.u.b	$8$	$0$	$2$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{6}]$