Space of modular forms of level 23, weight 6, and Character 23.c

• Label: 23.6.c
• Level: $23$
• Weight: $6$
• Character orbit: 23.c
• Rep. character: $\chi_{23}(2,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $90$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(23, [\chi])\).

	Total	New	Old
Modular forms	110	110	0
Cusp forms	90	90	0
Eisenstein series	20	20	0

Trace form

\( 90 q - 11 q^{2} - 7 q^{3} - 139 q^{4} + 5 q^{5} - 148 q^{6} - 29 q^{7} - 44 q^{8} - 894 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(23, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
23.6.c.a	$23$	$6$	23.c	23.c	$11$	$90$	$9$	$3.689$		None		$2$	$0$	\(-11\)	\(-7\)	\(5\)	\(-29\)		$\mathrm{SU}(2)[C_{11}]$