Space of modular forms of level 473, weight 2, and Character 473.i

• Label: 473.2.i
• Level: $473$
• Weight: $2$
• Character orbit: 473.i
• Rep. character: $\chi_{473}(252,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $84$
• Newform subspaces: $1$
• Sturm bound: $88$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 473 = 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	473.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 473 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(88\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(473, [\chi])\).

	Total	New	Old
Modular forms	92	92	0
Cusp forms	84	84	0
Eisenstein series	8	8	0

Trace form

\( 84 q - 6 q^{3} + 76 q^{4} - 6 q^{5} + 48 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(473, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
473.2.i.a	$473$	$2$	473.i	473.i	$6$	$84$	$42$	$3.777$		None		$4$	$0$	\(0\)	\(-6\)	\(-6\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$