Space of modular forms of level 23, weight 19, and Character 23.b

• Label: 23.19.b
• Level: $23$
• Weight: $19$
• Character orbit: 23.b
• Rep. character: $\chi_{23}(22,\cdot)$
• Character field: $\Q$
• Dimension: $35$
• Newform subspaces: $3$
• Sturm bound: $38$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 19 \)
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:			\(38\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(23, [\chi])\).

	Total	New	Old
Modular forms	37	37	0
Cusp forms	35	35	0
Eisenstein series	2	2	0

Trace form

35 * q + 168 * q^2 - 20130 * q^3 + 4092072 * q^4 + 2318115 * q^6 + 18825195 * q^8 + 4214797041 * q^9 - 5321755797 * q^12 - 655768946 * q^13 + 365919226384 * q^16 + 450489495579 * q^18 + 874880797443 * q^23 + 3021614025360 * q^24 - 3292642113085 * q^25 - 8213187707757 * q^26 - 7982123901036 * q^27 - 30667383347322 * q^29 + 61916976271654 * q^31 + 63545537188608 * q^32 - 97946624844120 * q^35 + 43210700594931 * q^36 + 111220720631940 * q^39 - 1087883639418714 * q^41 - 117414370775936 * q^46 - 770876632573578 * q^47 + 5112458972709003 * q^48 - 887909137819669 * q^49 + 3736249695919320 * q^50 - 2679946447733133 * q^52 - 3496693109910885 * q^54 - 8166714828852600 * q^55 - 18542223059304901 * q^58 - 14548975815379986 * q^59 + 5362886014107123 * q^62 + 22809068034472883 * q^64 - 64256080760341770 * q^69 + 46870559804852640 * q^70 + 31512883516333086 * q^71 + 136174746487938147 * q^72 + 58247715757776334 * q^73 - 89535755592176010 * q^75 + 250183815829725672 * q^77 - 564072937379856909 * q^78 + 25788506735558295 * q^81 - 501607580940050485 * q^82 + 490071094606517400 * q^85 - 194505376026720996 * q^87 - 1563136944458675832 * q^92 + 1843523091987505836 * q^93 + 1150778310490311179 * q^94 - 621924523779350640 * q^95 + 2865042234791107035 * q^96 - 1959791456322602664 * q^98

Decomposition of \(S_{19}^{\mathrm{new}}(23, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
23.19.b.a	$23$	$19$	23.b	23.b	$2$	$1$	$1$	$47.239$	\(\Q\)	\(\Q(\sqrt{-23}) \)	✓	✓			23.19.b.a	$2$	$0$	\(1001\)	\(28234\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+1001q^{2}+28234q^{3}+739857q^{4}+\cdots\)
23.19.b.b	$23$	$19$	23.b	23.b	$2$	$2$	$2$	$47.239$	\(\Q(\sqrt{69}) \)	\(\Q(\sqrt{-23}) \)	✓	✓			23.19.b.b	$2$	$0$	\(-1001\)	\(-28234\)	\(0\)	\(0\)	$5$	$\mathrm{U}(1)[D_{2}]$	\(q+(-505-9\beta )q^{2}+(-14689-1144\beta )q^{3}+\cdots\)
23.19.b.c	$23$	$19$	23.b	23.b	$2$	$32$	$32$	$47.239$		None		✓	✓		23.19.b.c	$2$	$0$	\(168\)	\(-20130\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$