Space of modular forms of level 520, weight 2, and Character 520.ca

• Label: 520.2.ca
• Level: $520$
• Weight: $2$
• Character orbit: 520.ca
• Rep. character: $\chi_{520}(101,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $112$
• Newform subspaces: $2$
• Sturm bound: $168$
• Trace bound: $4$

Defining parameters

Level:	$N$	$=$	$520 = 2^{3} \cdot 5 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	520.ca (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$104$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$2$
Sturm bound:			$168$
Trace bound:			$4$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(520, [\chi])$.

	Total	New	Old
Modular forms	176	112	64
Cusp forms	160	112	48
Eisenstein series	16	0	16

Trace form

112 * q - 18 * q^6 + 56 * q^9 + 12 * q^12 - 8 * q^14 + 4 * q^16 + 12 * q^20 - 12 * q^22 + 24 * q^23 + 24 * q^24 + 112 * q^25 - 26 * q^26 - 6 * q^28 - 8 * q^30 - 30 * q^32 - 6 * q^36 - 48 * q^39 - 32 * q^42 - 30 * q^46 - 48 * q^48 + 40 * q^49 - 46 * q^52 - 54 * q^54 - 16 * q^55 + 38 * q^56 - 48 * q^58 + 8 * q^62 - 60 * q^64 + 28 * q^66 - 18 * q^68 - 132 * q^72 + 68 * q^74 - 108 * q^76 + 108 * q^78 + 24 * q^80 - 56 * q^81 - 30 * q^84 - 72 * q^87 + 22 * q^88 + 36 * q^90 - 36 * q^92 + 2 * q^94 - 32 * q^95 + 48 * q^97 + 84 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(520, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
520.2.ca.a	$520$	$2$	520.ca	104.s	$6$	$56$	$28$	$4.152$		None		✓			520.2.ca.a	$2$	$0$	$0$	$0$	$-56$	$0$		$\mathrm{SU}(2)[C_{6}]$
520.2.ca.b	$520$	$2$	520.ca	104.s	$6$	$56$	$28$	$4.152$		None		✓			520.2.ca.a	$2$	$0$	$0$	$0$	$56$	$0$		$\mathrm{SU}(2)[C_{6}]$

Decomposition of $S_{2}^{\mathrm{old}}(520, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(520, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(104, [\chi])$$^{\oplus 2}$