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

• Label: 483.2.u
• Level: $483$
• Weight: $2$
• Character orbit: 483.u
• Rep. character: $\chi_{483}(113,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $480$
• 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.u (of order $22$ and degree $10$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$69$
Character field:			$\Q(\zeta_{22})$
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	680	480	200
Cusp forms	600	480	120
Eisenstein series	80	0	80

Trace form

480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

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.u.a	$483$	$2$	483.u	69.g	$22$	$480$	$48$	$3.857$		None		✓	✓	✓	483.2.u.a	$4$	$0$	$0$	$4$	$0$	$0$		$\mathrm{SU}(2)[C_{22}]$

Decomposition of $S_{2}^{\mathrm{old}}(483, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(483, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(69, [\chi])$$^{\oplus 2}$