Space of modular forms of level 483, weight 3, and Character 483.g

• Label: 483.3.g
• Level: $483$
• Weight: $3$
• Character orbit: 483.g
• Rep. character: $\chi_{483}(139,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	483.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(483, [\chi])\).

	Total	New	Old
Modular forms	132	60	72
Cusp forms	124	60	64
Eisenstein series	8	0	8

Trace form

\( 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(483, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
483.3.g.a	$483$	$3$	483.g	7.b	$2$	$60$	$60$	$13.161$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(483, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(483, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)