Space of modular forms of level 23, weight 7, and Character 23.b

• Label: 23.7.b
• Level: $23$
• Weight: $7$
• Character orbit: 23.b
• Rep. character: $\chi_{23}(22,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $3$
• Sturm bound: $14$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	23.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(14\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(23, [\chi])\).

	Total	New	Old
Modular forms	13	13	0
Cusp forms	11	11	0
Eisenstein series	2	2	0

Trace form

\( 11 q + 8 q^{2} + 30 q^{3} + 360 q^{4} - 285 q^{6} + 475 q^{8} + 633 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(23, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
23.7.b.a	$23$	$7$	23.b	23.b	$2$	$1$	$1$	$5.291$	\(\Q\)	\(\Q(\sqrt{-23}) \)	✓	✓			23.7.b.a	$2$	$0$	\(-7\)	\(-38\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-7q^{2}-38q^{3}-15q^{4}+266q^{6}+\cdots\)
23.7.b.b	$23$	$7$	23.b	23.b	$2$	$2$	$2$	$5.291$	\(\Q(\sqrt{69}) \)	\(\Q(\sqrt{-23}) \)	✓	✓			23.7.b.b	$2$	$0$	\(7\)	\(38\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(2+3\beta )q^{2}+(23-8\beta )q^{3}+(93+21\beta )q^{4}+\cdots\)
23.7.b.c	$23$	$7$	23.b	23.b	$2$	$8$	$8$	$5.291$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓	✓		23.7.b.c	$2$	$0$	\(8\)	\(30\)	\(0\)	\(0\)	$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{1})q^{2}+(4+\beta _{3})q^{3}+(21-3\beta _{1}+\cdots)q^{4}+\cdots\)