Space of modular forms of level 23, weight 13, and Character 23.b

• Label: 23.13.b
• Level: $23$
• Weight: $13$
• Character orbit: 23.b
• Rep. character: $\chi_{23}(22,\cdot)$
• Character field: $\Q$
• Dimension: $23$
• Newform subspaces: $3$
• Sturm bound: $26$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 13 \)
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:			\(26\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(23, [\chi])\).

	Total	New	Old
Modular forms	25	25	0
Cusp forms	23	23	0
Eisenstein series	2	2	0

Trace form

\( 23 q + 88 q^{2} + 318 q^{3} + 48360 q^{4} + 45651 q^{6} + 665411 q^{8} + 3565749 q^{9} + O(q^{10}) \)

Decomposition of \(S_{13}^{\mathrm{new}}(23, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
23.13.b.a	$23$	$13$	23.b	23.b	$2$	$1$	$1$	$21.022$	\(\Q\)	\(\Q(\sqrt{-23}) \)	✓	✓			23.13.b.a	$2$	$0$	\(-79\)	\(-14\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-79q^{2}-14q^{3}+2145q^{4}+1106q^{6}+\cdots\)
23.13.b.b	$23$	$13$	23.b	23.b	$2$	$2$	$2$	$21.022$	\(\Q(\sqrt{69}) \)	\(\Q(\sqrt{-23}) \)	✓	✓			23.13.b.b	$2$	$0$	\(79\)	\(14\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(29+21\beta )q^{2}+(159-304\beta )q^{3}+\cdots\)
23.13.b.c	$23$	$13$	23.b	23.b	$2$	$20$	$20$	$21.022$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		23.13.b.c	$2$	$0$	\(88\)	\(318\)	\(0\)	\(0\)	$2^{35}\cdot 3^{11}\cdot 67$	$\mathrm{SU}(2)[C_{2}]$	\(q+(4+\beta _{1})q^{2}+(15+2\beta _{1}-\beta _{3})q^{3}+\cdots\)