Properties

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 $1$

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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

\( 71 q - 169832 q^{2} + 420071358 q^{3} + 2439865505256 q^{4} + 4961334023571 q^{6} + 36321850216539491 q^{8} + 3351020573904674853 q^{9} + O(q^{10}) \) \( 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} + O(q^{100}) \)

Decomposition of \(S_{37}^{\mathrm{new}}(23, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
23.37.b.a 23.b 23.b $1$ $188.810$ \(\Q\) \(\Q(\sqrt{-23}) \) 23.37.b.a \(477713\) \(22317778\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+477713q^{2}+22317778q^{3}+159490233633q^{4}+\cdots\)
23.37.b.b 23.b 23.b $2$ $188.810$ \(\Q(\sqrt{69}) \) \(\Q(\sqrt{-23}) \) 23.37.b.b \(-477713\) \(-22317778\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-239266-819\beta )q^{2}+(-12627057+\cdots)q^{3}+\cdots\)
23.37.b.c 23.b 23.b $68$ $188.810$ None 23.37.b.c \(-169832\) \(420071358\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$