Space of modular forms of level 479, weight 2, and Character 479.c

• Label: 479.2.c
• Level: $479$
• Weight: $2$
• Character orbit: 479.c
• Rep. character: $\chi_{479}(2,\cdot)$
• Character field: $\Q(\zeta_{239})$
• Dimension: $9282$
• Newform subspaces: $1$
• Sturm bound: $80$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 479 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	479.c (of order \(239\) and degree \(238\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 479 \)
Character field:			\(\Q(\zeta_{239})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(80\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(479, [\chi])\).

	Total	New	Old
Modular forms	9758	9758	0
Cusp forms	9282	9282	0
Eisenstein series	476	476	0

Trace form

\( 9282 q - 237 q^{2} - 237 q^{3} - 275 q^{4} - 235 q^{5} - 233 q^{6} - 235 q^{7} - 227 q^{8} - 274 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(479, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
479.2.c.a	$479$	$2$	479.c	479.c	$239$	$9282$	$39$	$3.825$		None		✓	✓	✓	479.2.c.a	$2$	$0$	\(-237\)	\(-237\)	\(-235\)	\(-235\)		$\mathrm{SU}(2)[C_{239}]$