Space of modular forms of level 23, weight 3, and Character 23.d

• Label: 23.3.d
• Level: $23$
• Weight: $3$
• Character orbit: 23.d
• Rep. character: $\chi_{23}(5,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $30$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	23.d (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(23, [\chi])\).

	Total	New	Old
Modular forms	50	50	0
Cusp forms	30	30	0
Eisenstein series	20	20	0

Trace form

\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(23, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
23.3.d.a	$23$	$3$	23.d	23.d	$22$	$30$	$3$	$0.627$		None		$2$	$0$	\(-11\)	\(-11\)	\(-11\)	\(-11\)		$\mathrm{SU}(2)[C_{22}]$