Space of modular forms of level 483, weight 2, and Character 483.bb

• Label: 483.2.bb
• Level: $483$
• Weight: $2$
• Character orbit: 483.bb
• Rep. character: $\chi_{483}(26,\cdot)$
• Character field: $\Q(\zeta_{66})$
• Dimension: $1200$
• Newform subspaces: $1$
• Sturm bound: $128$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$483 = 3 \cdot 7 \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	483.bb (of order $66$ and degree $20$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$483$
Character field:			$\Q(\zeta_{66})$
Newform subspaces:			$1$
Sturm bound:			$128$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(483, [\chi])$.

	Total	New	Old
Modular forms	1360	1360	0
Cusp forms	1200	1200	0
Eisenstein series	160	160	0

Trace form

1200 * q - 27 * q^3 - 74 * q^4 - 36 * q^7 - 13 * q^9 - 54 * q^10 - 15 * q^12 - 64 * q^15 + 38 * q^16 + 43 * q^18 - 54 * q^19 - 70 * q^21 - 160 * q^22 - 66 * q^24 + 34 * q^25 - 76 * q^28 - 23 * q^30 - 54 * q^31 - 3 * q^33 - 28 * q^36 + 26 * q^37 + 5 * q^39 - 30 * q^40 - 68 * q^42 - 176 * q^43 - 96 * q^45 - 22 * q^46 - 128 * q^49 - 23 * q^51 - 102 * q^52 + 21 * q^54 - 36 * q^57 + 58 * q^58 - 43 * q^60 - 126 * q^61 + 41 * q^63 + 40 * q^64 - 132 * q^66 - 10 * q^67 + 20 * q^70 + 59 * q^72 - 30 * q^73 - 81 * q^75 + 164 * q^78 - 14 * q^79 - 97 * q^81 - 66 * q^82 + 24 * q^84 - 56 * q^85 - 399 * q^87 - 74 * q^88 - 156 * q^91 + 8 * q^93 - 126 * q^94 - 117 * q^96 + 196 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(483, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
483.2.bb.a	$483$	$2$	483.bb	483.ab	$66$	$1200$	$60$	$3.857$		None		✓	✓	✓	483.2.bb.a	$8$	$0$	$0$	$-27$	$0$	$-36$		$\mathrm{SU}(2)[C_{66}]$