Space of modular forms of level 23, weight 8, and Character 23.c

• Label: 23.8.c
• Level: $23$
• Weight: $8$
• Character orbit: 23.c
• Rep. character: $\chi_{23}(2,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $130$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
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:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(23, [\chi])\).

	Total	New	Old
Modular forms	150	150	0
Cusp forms	130	130	0
Eisenstein series	20	20	0

Trace form

\( 130 q + 5 q^{2} + 17 q^{3} - 907 q^{4} - 399 q^{5} + 1196 q^{6} - 301 q^{7} + 2764 q^{8} - 11694 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(23, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
23.8.c.a	$23$	$8$	23.c	23.c	$11$	$130$	$13$	$7.185$		None		$2$	$0$	\(5\)	\(17\)	\(-399\)	\(-301\)		$\mathrm{SU}(2)[C_{11}]$