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

• Label: 473.2.bc
• Level: $473$
• Weight: $2$
• Character orbit: 473.bc
• Rep. character: $\chi_{473}(9,\cdot)$
• Character field: $\Q(\zeta_{105})$
• Dimension: $2016$
• Newform subspaces: $1$
• Sturm bound: $88$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 473 = 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	473.bc (of order \(105\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 473 \)
Character field:			\(\Q(\zeta_{105})\)
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	2208	2208	0
Cusp forms	2016	2016	0
Eisenstein series	192	192	0

Trace form

\( 2016 q - 30 q^{2} - 35 q^{3} + 54 q^{4} - 35 q^{5} - 28 q^{6} - 39 q^{7} - 36 q^{8} - 65 q^{9} + O(q^{10}) \)

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.bc.a	$473$	$2$	473.bc	473.ac	$105$	$2016$	$42$	$3.777$		None		$4$	$0$	\(-30\)	\(-35\)	\(-35\)	\(-39\)		$\mathrm{SU}(2)[C_{105}]$