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 + 80143358001671045739 * q^12 - 138225739750874655842 * q^13 + 65048794803903138411280 * q^16 + 110695487945300555217459 * q^18 - 5207172329400446790884521 * q^23 + 16406035806036921908358912 * q^24 - 231610323121418323620220537 * q^25 + 108808319099889814899665147 * q^26 + 132787034118723393447495276 * q^27 - 558199461974868765864673202 * q^29 + 599363078257095479091573550 * q^31 + 3190837213535635784923715424 * q^32 + 12078867004231477963993992432 * q^35 + 133808843032975441094807133075 * q^36 + 151731208408929743590949278956 * q^39 - 151630657412261041969764873266 * q^41 - 80201724177451070868265295984 * q^46 - 7550969334439352730076522249202 * q^47 + 3877902006655681029850237511235 * q^48 - 31655519469483461426100634006249 * q^49 - 29126377783846026445198006057160 * q^50 - 5118224559419672932017211933461 * q^52 - 44332735155962733709623793222893 * q^54 + 63985059845657433229983699796848 * q^55 - 293439719828784124648080005631349 * q^58 - 184708126353444507519719517369794 * q^59 + 474318784779133156202086012330691 * q^62 + 2600480930943422685188586152652995 * q^64 + 4746086623125586280265001671385518 * q^69 - 5531498034172547484862621124634096 * q^70 - 2215566464115265646139105420294146 * q^71 + 22294785821004136914833890792881603 * q^72 - 6447226941649928093117183082393122 * q^73 + 1409948377440361040061449961023118 * q^75 + 11835328662707567321553872923743120 * q^77 + 120504679009199670748133367926802387 * q^78 + 62143656116216019218459792489274867 * q^81 + 92811647528839965927942657092700491 * q^82 + 208401262573962605156448943117063536 * q^85 - 393138762491918984293678684177071684 * q^87 - 1590605649912734160342480805161521928 * q^92 - 412862513419607415542379800401675044 * q^93 - 2723955905463011673836281863661707277 * q^94 + 257492951778787971819423543869677344 * q^95 + 273190976530497600750981159326891763 * q^96 + 551632103991822184229032166091464728 * q^98

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	$2$	$0$	$-169832$	$420071358$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$