Space of modular forms of level 23, weight 37, and Character 23.b

• Label: 23.37.b
• Level: $23$
• Weight: $37$
• Character orbit: 23.b
• Rep. character: $\chi_{23}(22,\cdot)$
• Character field: $\Q$
• Dimension: $71$
• Newform subspaces: $3$
• Sturm bound: $74$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 37 \)
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:			\(74\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{37}(23, [\chi])\).

	Total	New	Old
Modular forms	73	73	0
Cusp forms	71	71	0
Eisenstein series	2	2	0

Trace form

\( 71 q - 169832 q^{2} + 420071358 q^{3} + 2439865505256 q^{4} + 4961334023571 q^{6} + 36321850216539491 q^{8} + 3351020573904674853 q^{9} + O(q^{10}) \)

Decomposition of \(S_{37}^{\mathrm{new}}(23, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
23.37.b.a	$23$	$37$	23.b	23.b	$2$	$1$	$1$	$188.810$	\(\Q\)	\(\Q(\sqrt{-23}) \)	✓	✓			23.37.b.a	$2$	$0$	\(477713\)	\(22317778\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+477713q^{2}+22317778q^{3}+159490233633q^{4}+\cdots\)
23.37.b.b	$23$	$37$	23.b	23.b	$2$	$2$	$2$	$188.810$	\(\Q(\sqrt{69}) \)	\(\Q(\sqrt{-23}) \)	✓	✓			23.37.b.b	$2$	$0$	\(-477713\)	\(-22317778\)	\(0\)	\(0\)	$5\cdot 11$	$\mathrm{U}(1)[D_{2}]$	\(q+(-239266-819\beta )q^{2}+(-12627057+\cdots)q^{3}+\cdots\)
23.37.b.c	$23$	$37$	23.b	23.b	$2$	$68$	$68$	$188.810$		None		✓	✓		23.37.b.c	$2$	$0$	\(-169832\)	\(420071358\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$