Space of modular forms of level 23, weight 15, and Character 23.b

• Label: 23.15.b
• Level: $23$
• Weight: $15$
• Character orbit: 23.b
• Rep. character: $\chi_{23}(22,\cdot)$
• Character field: $\Q$
• Dimension: $27$
• Newform subspaces: $2$
• Sturm bound: $30$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	23.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(30\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(23, [\chi])\).

	Total	New	Old
Modular forms	29	29	0
Cusp forms	27	27	0
Eisenstein series	2	2	0

Trace form

\( 27 q - 184 q^{2} - 2160 q^{3} + 184104 q^{4} - 44733 q^{6} - 7241669 q^{8} + 39199155 q^{9} + O(q^{10}) \)

Decomposition of \(S_{15}^{\mathrm{new}}(23, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
23.15.b.a	$23$	$15$	23.b	23.b	$2$	$3$	$3$	$28.596$	3.3.621.1	\(\Q(\sqrt{-23}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(13\beta _{1}-71\beta _{2})q^{2}+(622\beta _{1}-1057\beta _{2})q^{3}+\cdots\)
23.15.b.b	$23$	$15$	23.b	23.b	$2$	$24$	$24$	$28.596$		None		$2$	$0$	\(-184\)	\(-2160\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$