Space of modular forms of level 23, weight 25, and Character 23.b

• Label: 23.25.b
• Level: $23$
• Weight: $25$
• Character orbit: 23.b
• Rep. character: $\chi_{23}(22,\cdot)$
• Character field: $\Q$
• Dimension: $47$
• Newform subspaces: $3$
• Sturm bound: $50$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 25 \)
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:			\(50\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{25}(23, [\chi])\).

	Total	New	Old
Modular forms	49	49	0
Cusp forms	47	47	0
Eisenstein series	2	2	0

Trace form

\( 47 q - 4232 q^{2} - 434562 q^{3} + 368092008 q^{4} - 5593673229 q^{6} + 74005246931 q^{8} + 5067330597741 q^{9} + O(q^{10}) \)

Decomposition of \(S_{25}^{\mathrm{new}}(23, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
23.25.b.a	$23$	$25$	23.b	23.b	$2$	$1$	$1$	$83.942$	\(\Q\)	\(\Q(\sqrt{-23}) \)	✓	✓			23.25.b.a	$2$	$0$	\(-1951\)	\(-1062686\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-1951q^{2}-1062686q^{3}-12970815q^{4}+\cdots\)
23.25.b.b	$23$	$25$	23.b	23.b	$2$	$2$	$2$	$83.942$	\(\Q(\sqrt{69}) \)	\(\Q(\sqrt{-23}) \)	✓	✓			23.25.b.b	$2$	$0$	\(1951\)	\(1062686\)	\(0\)	\(0\)	$7$	$\mathrm{U}(1)[D_{2}]$	\(q+(1094+237\beta )q^{2}+(531039-608\beta )q^{3}+\cdots\)
23.25.b.c	$23$	$25$	23.b	23.b	$2$	$44$	$44$	$83.942$		None		✓	✓		23.25.b.c	$2$	$0$	\(-4232\)	\(-434562\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$