Space of modular forms of level 23, weight 4, and Character 23.c

• Label: 23.4.c
• Level: $23$
• Weight: $4$
• Character orbit: 23.c
• Rep. character: $\chi_{23}(2,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $50$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	23.c (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(23, [\chi])\).

	Total	New	Old
Modular forms	70	70	0
Cusp forms	50	50	0
Eisenstein series	20	20	0

Trace form

\( 50 q - 11 q^{2} - 13 q^{3} - 27 q^{4} - 19 q^{5} - 4 q^{6} - 19 q^{7} + 28 q^{8} + 24 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(23, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
23.4.c.a	$23$	$4$	23.c	23.c	$11$	$50$	$5$	$1.357$		None		$2$	$0$	\(-11\)	\(-13\)	\(-19\)	\(-19\)		$\mathrm{SU}(2)[C_{11}]$