Space of modular forms of level 23, weight 29, and Character 23.b

• Label: 23.29.b
• Level: $23$
• Weight: $29$
• Character orbit: 23.b
• Rep. character: $\chi_{23}(22,\cdot)$
• Character field: $\Q$
• Dimension: $55$
• Newform subspaces: $2$
• Sturm bound: $58$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 29 \)
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:			\(58\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{29}(23, [\chi])\).

	Total	New	Old
Modular forms	57	57	0
Cusp forms	55	55	0
Eisenstein series	2	2	0

Trace form

55 * q + 15832 * q^2 - 5427372 * q^3 + 7252157160 * q^4 - 212012223021 * q^6 - 1244821327357 * q^8 + 345647825074395 * q^9 - 2074563934608021 * q^12 - 1758658971151684 * q^13 + 1021509801019713296 * q^16 - 287771517071500461 * q^18 + 8768542050103687103 * q^23 - 110598531749208223680 * q^24 - 323677297149900498737 * q^25 - 207979385965689394981 * q^26 - 305862948399683629590 * q^27 + 925659140035412038660 * q^29 + 2703701778405230160716 * q^31 - 791115532328224542240 * q^32 + 13251818601033282860472 * q^35 + 36564875568076951974675 * q^36 + 89346733985574038370354 * q^39 - 132326893146221239433564 * q^41 - 4863375048584916290992 * q^46 + 574182550634754586280764 * q^47 - 3600090350285167978600221 * q^48 - 1523343589635094552264241 * q^49 - 1860224368694476604730440 * q^50 + 1372975351323703729100427 * q^52 - 1815309672459866279016525 * q^54 + 10306783952635767615407688 * q^55 - 15479234695899146866810805 * q^58 + 13760335936219388994449518 * q^59 + 31000816007583979572925571 * q^62 + 163037511229933868749972099 * q^64 - 70504575256868426624529132 * q^69 + 250927446357728400824191824 * q^70 - 135440529049032505794489164 * q^71 - 1004914771059804830393687997 * q^72 + 125710073933169045570594476 * q^73 - 189883557682412666980357812 * q^75 - 565144786411247786889787704 * q^77 - 1043051847980745824783186349 * q^78 + 1838115302273237910842613351 * q^81 + 2919024814780148981388441163 * q^82 - 22138349294173438915247784 * q^85 + 2954515181663846373711718410 * q^87 + 13796114477425383648075117624 * q^92 - 13283019104233677979173518550 * q^93 - 1593756264624383628604004141 * q^94 - 1563041729354939535820795776 * q^95 + 11350798982531164032212480019 * q^96 - 48517320786468480501661009640 * q^98

Decomposition of \(S_{29}^{\mathrm{new}}(23, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
23.29.b.a	$23$	$29$	23.b	23.b	$2$	$3$	$3$	$114.237$	3.3.621.1	\(\Q(\sqrt{-23}) \)	✓	✓			23.29.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-11759\beta _{1}-3026\beta _{2})q^{2}+(-3162522\beta _{1}+\cdots)q^{3}+\cdots\)
23.29.b.b	$23$	$29$	23.b	23.b	$2$	$52$	$52$	$114.237$		None		✓	✓		23.29.b.b	$2$	$0$	\(15832\)	\(-5427372\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$